The Weight Distribution of Quasi-quadratic Residue Codes

The Weight Distribution of Quasi-quadratic Residue Codes

Let Aut( ˆ

Qp)PSL2(p) = H, the number of weight jcodewords Aj

can be categorised into two classes:one which contains all weight jcode-

words that are invariant under some element of Handanother which con

tains the rest.Given a codeword ofˆ

Qpthat is not invariant under some

element of H,applying all|H| =1

2p(p21) permutations will result in |H|

distinct codewords ofˆ

Qp.In other words, the latter class forms orbits of size

equal to the cardinality of PSL2(p).Let Aj(H)denote the number of weight

jcodewords which areinvariant under someelement ofH, we may write

Aj=nj· |H| Aj(H)

Aj(H)(mod 1

2p(p21)) (3)

for njZ={0} ∪ Z i.e. non negative integer.Since |H| can be factorised

as H=Qiqei

iwhere qiis a prime and eiis apositive integer, it is shown in

[6] that Aj(H)may be obtained by applying the Chinese Remainder The-

orem to Aj(Sqi)(mod qei

i)for all primes qithatdivide |H|.Note that Sqi

is the Sylow-qi-subgroup of Hand Aj(Sqi)is thenumber of codewords of

weight jfixed by someelement ofSqi.

For each prime qi, in order tocompute Aj(Sqi), the subcode which is

invariant under some element of Sqineeds to be obtained.For oddprimes

qi,Sqiis cyclic and there exists a b

cd ∈ H, for some integers a, b, c, d, which

generates cyclic permutation oforder qi.Thus, itisstraightforward to ob-

tain theinvariantsubcodeandthecorresponding Aj(Sqi).On the other

hand, if qi= 2,S2is a dihedral group of order 2s,where sis the highest

power of 2that divides |H|, and Aj(S2)is given by [6]

Aj(S2)(2s1 1)Aj(H2)2s2Aj(G0

4)2s2Aj(G1

4)(mod 2s),(4)

where H2and Gi

4, for i= 0,1, aresubgroups of order 2and 4respectively,

which are contained in S2.Let PH of order 2s1and T=01

10 ∈ H of

order 2, it is shown in [6] that H2={1, P 2s2}and thenon cyclic subgroup

Gi

4={1, P 2s2, P iT , P 2s2 iT}.

4The Weight Distribution

Following Gleason’s theorem, see (2), the weight distribution of the binary

extended QR code ofprime 137 is given by

Aˆ

Q137 (z) =

17

X

j=0

Kj(1 z2)694j(z22z4 z6)j.(5)

Since A0= 1 and the minimum distance ofˆ

Q137 is 22, only A2j, for 11 j

17, are required inorder todeduce Aˆ

Q137 (z)completely. Note that each A2j

determines Kjfor some integer j.However, following the idea in [6] which

has been relatively forgotten, K17 may bedetermined without the need of

exhaustively computing A34 as shown in this section.

Let us firstdeduce themodular congruence ofA2j, for 11 j17, of

ˆ

Q137.Some of these congruences have been given in the authors’ previous

4

We investigate a family of codes called quasi-quadratic residue (QQR) codes. We are interested in these codes mainly for two reasons: Firstly, they have close relations with hyperelliptic curves and Goppa’s Conjecture, and serve as a strong tool in studying those objects. Secondly, they are very good codes. Computational results show they have large minimum distances when $pequiv 3 pmod 8$.

Our studies focus on the weight distributions of these codes. We will prove a new discovery about their weight polynomials, i.e. they are divisible by $(x^2 y^2)^{d-1}$, where $d$ is the corresponding minimum distance. We also show that the weight distributions of these codes are asymptotically normal. Based on the relation between QQR codes and hyperelliptic curves, we will also prove a result on the point distribution on hyperelliptic curves.

Mathematics Subject Classification: Primary: 94B15, 94B60; Secondary: 11G20.

A015064 Weight distribution of [50,21,12] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 0, 0, 1050, 925, 21875, 68250, 169925, 333300, 453250, 453250, 333300, 169925, 68250, 21875, 925, 1050, 0, 0, 0, 0, 0, 1

A015065 Weight distribution of [50,29,8] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 800, 8295, 114625, 920175, 4627875, 17257800, 45069885, 84369875, 116066125, 116066125, 84369875, 45069885, 17257800, 4627875, 920175, 114625, 8295, 800, 0, 0, 0, 1

A015066 Weight distribution of [50,22,7] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 1050, 0, 925, 12700, 21875, 34300, 68250, 107800, 169925, 258000, 333300, 404250, 453250, 462952, 453250, 404250, 333300, 258000, 169925, 107800, 68250, 34300, 21875, 12700, 925, 0, 1050, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 1

A015067 Weight distribution of [50,28,8] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 750, 7770, 52675, 449550, 2311575, 8624700, 22661835, 42102850, 57811425, 58254700, 42267025, 22408050, 8633100, 2316300, 470625, 61950, 525, 50, 0, 0, 0, 1

A015068 Weight distribution of [100,22,22] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 1100, 3850, 0, 4125, 38500, 92400, 193600, 347600, 485100, 600600, 660352, 600600, 485100, 347600, 193600, 92400, 38500, 4125, 0, 3850, 1100, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A015069 Weight distribution of [100,78,6] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 3850, 0, 8625540, 504741475, 21060732550, 641604305375, 14622264133400, 255578801503795, 3496197414021950, 38040184865580975, 333583288959605300, 2383620258950558925, 14005822677643540370, 68193674451079227050, 276907651030419444000, 942804612331379390725, 2703690041528811696900, 6554715235199646035290, 13474850115575617584200, 23545377618939915393150, 35033702002644035359900, 44444350668327576562750, 48108741996656177342352

A015070 Weight distribution of [100,22,32] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3850, 5600, 4125, 0, 92400, 387200, 347600, 0, 600600, 1311552, 600600, 0, 347600, 387200, 92400, 0, 4125, 5600, 3850, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A015071 Weight distribution of [100,78,8] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 137225, 7231840, 511741475, 20997046400, 642104180575, 14620696059200, 255580729090995, 3496191224323200, 38040223036760175, 333583215539666400, 2383620193904285325, 14005823013894187520, 68193674589734420650, 276907649362395385600, 942804613467381809925, 2703690046024936460800, 6554715226694274576090, 13474850114631510264000, 23545377636355278743550, 35033701987289528723200, 44444350658167367673150, 48108742023087188141952

A002617 Weight distribution of Cheng-Sloane [ 32,17,8 ] code.

1, 0, 0, 0, 908, 3328, 14784, 27392, 38246, 27392, 14784, 3328, 908, 0, 0, 0, 1

A010031 Weight distribution of any one of the five doubly-even binary [32,16,8] codes (quadratic residue, Reed-Muller, etc.).

1, 0, 620, 13888, 36518, 13888, 620, 0, 1

A014488 Weight distribution of [ 17,9,7 ] code over GF(4).

1, 0, 0, 0, 0, 0, 0, 1224, 1530, 10200, 8160, 51408, 25704, 85680, 24480, 45288, 5661, 2808

A085518 One of the three possible weight distributions for a [16,7,6] binary code.

1, 0, 0, 45, 41, 34, 6, 1, 0

A085519 One of the three possible weight distributions for a [16,7,6] binary code.

1, 0, 0, 44, 45, 28, 10, 0, 0

A014487 Weight distribution of [ 18,9,8 ] self-dual code over GF(4).

1, 0, 0, 0, 2754, 18360, 77112, 110160, 50949, 2808

A018236 Weight distribution of hypothetical [ 72,36,16 ] doubly-even binary self-dual code.

1, 0, 0, 0, 249849, 18106704, 462962955, 4397342400, 16602715899, 25756721120, 16602715899, 4397342400, 462962955, 18106704, 249849, 0, 0, 0, 1

A018237 Weight distribution of hypothetical [ 68,34,12 ] code derived from hypothetical [ 72,36,16 ] doubly-even self-dual code.

1, 0, 0, 0, 0, 0, 442, 14960, 174471, 1478048, 9546537, 46699952, 175078410, 509477760, 1160564636, 2081169376, 2949602799, 3312254400, 2949602799, 2081169376, 1160564636, 509477760, 175078410, 46699952, 9546537, 1478048, 174471, 442, 0, 0, 0, 0, 0, 0, 1

A028299 Weight distribution of the dodecacode, a [12,0,6] quantum-error-correcting code.

1, 0, 0, 396, 1485, 1980, 234

A030030 Weight distribution of nonlinear binary (36,2^18,8) code.

1, 0, 0, 0, 306, 1530, 10608, 28152, 54621, 71708, 54621, 28152, 10608, 1530, 306, 0, 0, 0, 1

A030061 Weight distribution of [ 17,8,8 ] code over GF(4).

1, 0, 0, 0, 1530, 8160, 25704, 24480, 5661

A030062 Weight distribution of [ 96,48,12 ] doubly-even self-dual «octern» code.

1, 0, 0, 248, 9672, 3219288, 369688144, 18640824768, 422091297303, 4552776690944, 24292916390448, 65726628219120, 91448124030784, 65726628219120, 24292916390448, 4552776690944, 422091297303

A030331 Weight distribution of hypothetical [ 24,12,10 ] trace-self-dual additive code over GF(4).

1, 0, 0, 0, 0, 18216, 156492, 1147608, 3736557, 6248088, 4399164, 1038312, 32778

A131620 Weight distribution of a certain binary linear code of length 56 defined by AES (or Rijndael) S-box.

1, 0, 8, 27, 55, 240, 701, 1909, 5753, 15747, 41138, 104762, 252664, 580609, 1274691, 2665295, 5315469, 10113564, 18353698, 31781680, 52486460, 82606895, 123821091, 176518711, 238906435, 306378988, 371328696, 423932616

In this paper, we begin by reviewing some of the known properties of QQR codes and proved that $PSL_2(p)$ acts on the extended QQR code when $p equiv 3 pmod 4$. Using this discovery, we then showed their weight polynomials satisfy a strong divisibility condition, namely that they are divisible by $(x^2 y^2)^{d-1}$, where $d$ is the corresponding minimum distance. Using this result, we were able to construct an efficient algorithm to compute weight polynomials for QQR codes and correct errors in existing results on quadratic residue codes. In the second half, we use the relation between the weight of codewords and the number of points on hyperelliptic curves to prove that the symmetrized distribution of a set of hyperelliptic curves is asymptotically normal.

extended binary primitive BCH codes

(A-numbers A001381, A024881, A028381A028385, …, A145922A146888.)

A001381 Weight distribution of binary [ 48,24,12 ] quadratic residue code.

1, 0, 0, 17296, 535095, 3995376, 7681680, 3995376, 535095, 17296, 0, 0, 1

A024881 Weight distribution of [ 17,8,6 ] binary quadratic-residue code.

1, 0, 0, 68, 85, 68, 34

A028381 Weight distribution of [ 17,9,5 ] binary quadratic-residue code.

1, 0, 0, 0, 0, 34, 68, 68, 85, 85, 68, 68, 34, 0, 0, 0, 0, 1

A028382 Weight distribution of [ 31,16,7 ] binary BCH and quadratic-residue codes.

1, 0, 0, 0, 0, 0, 0, 155, 465, 0, 0, 5208, 8680, 0, 0, 18259, 18259, 0, 0, 8680, 5208, 0, 0, 465, 155, 0, 0, 0, 0, 0, 0, 1

A028383 Weight distribution of [ 31,15,8 ] binary quadratic-residue code.

1, 0, 465, 8680, 18259, 5208, 155

A028384 Weight distribution of [ 47,24,11 ] binary quadratic-residue code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4324, 12972, 0, 0, 178365, 356730, 0, 0, 1664740, 2330636, 0, 0, 3840840, 3840840, 0, 0, 2330636, 1664740, 0, 0, 356730, 178365, 0, 0, 12972, 4324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A028385 Weight distribution of [ 47,23,12 ] binary quadratic-residue code.

1, 0, 0, 12972, 356730, 2330636, 3840840, 1664740, 178365, 4324

A033869 Weight distribution of [79,40,15] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19513, 78052, 0, 0, 3220672, 9662016, 0, 0, 177021936, 413051184, 0, 0, 3705860928, 6882313152, 0, 0, 31883071220, 47824606830, 0, 0, 118486682496, 144817056384, 0, 0, 195553169504

A069646 Weight distribution of [97,49,15] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4656, 23862, 14841, 65960, 190120, 741468, 3375988, 11662504, 40893648, 126088748, 360406410, 998048520, 2614461952, 6536154880, 15589859400, 35337014640, 76345991760, 157463608005

A072189 Weight distribution of [103,52,19] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 218875, 919275, 0, 0, 47592180, 158640600, 0, 0, 4283380248, 11626317816, 0, 0, 174684872920, 393040964070, 0, 0, 3432179437380, 6483005603940, 0, 0, 33982965303425, 54372744485480

A076710 Weight distribution of [137,69,21] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 51238, 270164, 409904, 1947044, 4057118, 17476816, 99448300, 390689750, 1445284240, 5203023264, 18055712240, 59809546795, 189973513945, 581095454420, 1709208146190

A080953 Weight distribution of [151,76,19] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3775, 24915, 0, 0, 113250, 604000, 0, 0, 30256625, 133993625, 0, 0, 8292705580, 31097645925, 0, 0, 1302257122605, 4196161839505, 0, 0, 113402818847850, 317527892773980, 0

A091536 Weight distribution of [89,45,17] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54824, 219296, 626560, 2192960, 7462917, 23067198, 66429244, 182680421, 476804328, 1173672192, 2739870518, 6066856147, 12753805999, 25507611998, 48541216592

A106433 Weight distribution of [113,57,15] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3616, 22148, 79100, 371770, 539462, 2255932, 7723324, 28962465, 106963766, 362031208, 1164652580, 3577147210, 10584922440, 29637782832, 79257402672, 203097094347, 498291292415

A134975 Weight distribution of [127,64,19] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8890, 48006, 0, 0, 2416302, 10470642, 0, 0, 642229602, 2293677150, 0, 0, 80124107595, 240372322785, 0, 0, 5082581311830, 12988818908010, 0, 0, 172664602751130, 379862126052486, 0

A145922 Weight distribution of [71,36,13] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 497, 2485, 0, 0, 47570, 166495, 0, 0, 5084310, 13219206, 0, 0, 154102305, 308204610, 0, 0, 1710651635, 2688166855, 0, 0, 7377935180, 9222418975, 0, 0, 12879738244, 12879738244, 0, 0, 9222418975

A145981 Weight distribution of [71,36,11] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 497, 2485, 47570, 166495, 5084310, 13219206, 154102305, 308204610, 1710651635, 2688166855, 7377935180, 9222418975, 12879738244, 12879738244, 9222418975, 7377935180, 2688166855

A145982 Weight distribution of [73,37,13] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1533, 6570, 19272, 69861, 266085, 827820, 2292200, 6188940, 15841584, 37443744, 82642716, 172172325, 337713987, 623471976, 1086405418, 1784808901, 2766489030, 4057517244, 5630090544

A146075 Weight distribution of [41,21,9] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 410, 1312, 3034, 7585, 16605, 33210, 60024, 97539, 146370, 195160, 232060, 255266, 255266, 232060, 195160, 146370, 97539, 60024, 33210, 16605, 7585, 3034, 1312, 410, 0, 0, 0, 0, 0, 0, 0, 0, 1

A146888 Weight distribution of [167,84,23] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 110888, 665328, 0, 0, 3021698, 15108490, 0, 0, 1057206192, 4493126316, 0, 0, 268132007628, 983150694636, 0, 0, 39540857275985, 126530743283152, 0, 0

The first one below is special, thereafter all others are ordered by increasing A-numbers.

A120373 Weight distribution of [72,36,16] doubly-even binary self-dual extended quadratic-residue (or QR) code.

1, 0, 0, 2982, 214065, 18303516, 462306915, 4398818490, 16600354155, 25759476488, 16600354155, 4398818490, 462306915, 18303516, 214065, 2982, 0, 0, 1

A084554 Weight distribution of [104,52,20] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 1138150, 206232780, 15909698064, 567725836990, 9915185041320, 88355709788905, 413543821457520, 1036378989344140, 1406044530294756, 1036378989344140, 413543821457520, 88355709788905, 9915185041320

A097937 Weight distribution of [138,69,22] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321402, 2356948, 21533934, 490138050, 6648307504, 77865259035, 771068968365, 6551964560395, 48016671847203, 304734017875437, 1682222779056949, 8108674129521168

A098786 Weight distribution of [90,45,18] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 274120, 2819520, 30530115, 249109665, 1650476520, 8806726665, 38261417997, 136522171665, 402352364565, 983530112015, 2001805012350, 3403264592178, 4842229755990, 5773480681050

A142708 Weight distribution of [114,57,16] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 25764, 0, 450870, 2795394, 36685789, 468994974, 4741799790, 40222705272, 282354497019, 1670741392215, 8378734842802, 35791510616904, 130792381305999, 410299386601373, 1108537936510704

A145578 Weight distribution of [18,9,6] binary extended quadratic-residue (or QR) code.

1, 0, 0, 102, 153, 153, 102, 0, 0, 1

A145648 Weight distribution of [42,21,10] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 1722, 10619, 49815, 157563, 341530, 487326, 487326, 341530, 157563, 49815, 10619, 1722, 0, 0, 0, 0, 1

A145657 Weight distribution of [74,37,14] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 8103, 89133, 1093905, 8481140, 53285328, 254815041, 961185963, 2871214319, 6824006274, 13019584383, 19988042838, 24737670308, 24737670308, 19988042838, 13019584383, 6824006274

A145659 Weight distribution of [80,40,16] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 97565, 12882688, 590073120, 10588174080, 79707678050, 263303738880, 391106339008, 263303738880, 79707678050, 10588174080, 590073120, 12882688, 97565, 0, 0, 0, 1

A145683 Weight distribution of [98,49,16] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 28518, 80801, 931588, 15038492, 166982396, 1358454930, 9150616832, 50926874040, 233809599765, 894066458642, 2860927585152, 7695094033816, 17462837266490, 33526663755928, 54576674050892

A145685 Weight distribution of [120,60,20] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 56896, 12886944, 2935906752, 320496430380, 18071400219840, 552526728803616, 9491105395362624, 94116098389459776, 549827720843995776, 1920594821540759296, 4051982879111857664

A145686 Weight distribution of [152,76,20] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 28690, 717250, 164250250, 39390351505, 5498418962110, 430930711621830, 19714914846904500, 542987434093298560, 9222363801696269312, 98458872937331752960, 670740325520798121984

A145687 Weight distribution of [168,84,24] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 776216, 18130188, 5550332508, 1251282702264, 166071600559137, 13047136918828740, 629048543890724224, 19087130695796613120, 372099690249351069696, 4739291519495550533632

A010463 Weight distribution of [32,21,6] BCH code.

1, 0, 0, 992, 10540, 60512, 228160, 446400, 603942, 446400, 228160, 60512, 10540, 992, 0, 0, 1

A083488 Weight distribution of [127,99,9] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 62230, 734314, 8454390, 81725770, 706987918, 5756901618, 43470567491, 304293972437, 1986688064970, 12140871508150, 69649172729570, 376105532739678, 1916352155002274, 9233333110465502

A097479 Weight distribution of [127,50,27] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40894, 146050, 0, 0, 4853051, 14559153, 0, 0, 310454802, 793384494, 0, 0, 10538703840, 23185148448, 0, 0, 199123183160, 380144258760, 0, 0, 2154195406104

A111332 Weight distribution of [127,57,23] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112014, 485394, 0, 0, 5376672, 19202400, 0, 0, 609444171, 1828332513, 0, 0, 39831154272, 101790727584, 0, 0, 1348537052730, 2966781516006, 0, 0, 25489124479104

A151700 Weight distribution of [15,7,5] primitive binary BCH code.

1, 0, 0, 0, 0, 18, 30, 15, 15, 30, 18, 0, 0, 0, 0, 1

A151701 Weight distribution of [31,11,11] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 186, 310, 0, 0, 527, 527, 0, 0, 310, 186, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151713 Weight distribution of [63,10,27] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 252, 0, 0, 63, 63, 0, 0, 252, 196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151721 Weight distribution of [63,16,23] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1890, 3150, 0, 0, 5488, 7056, 0, 0, 15183, 15183, 0, 0, 7056, 5488, 0, 0, 3150, 1890, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151722 Weight distribution of [63,18,21] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1452, 2772, 1890, 3150, 9828, 14364, 5488, 7056, 32760, 37128, 15183, 15183, 37128, 32760, 7056, 5488, 14364, 9828, 3150, 1890, 2772, 1452, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151736 Weight distribution of [63,24,15] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 651, 1953, 3024, 7728, 0, 0, 74448, 142128, 109368, 182280, 668304, 976752, 388864, 499968, 2071440, 2347632, 914067, 914067, 2347632, 2071440, 499968, 388864, 976752, 668304, 182280, 109368

A151769 Weight distribution of [63,30,13] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1764, 6300, 7707, 23121, 177660, 454020, 352800, 776160, 4820112, 9202032, 5486040, 9143400, 42679728, 62378064, 28457632, 36588384, 132625080, 150308424, 53382483, 53382483, 150308424

A151770 Weight distribution of [63,36,11] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5670, 24570, 77616, 277200, 895755, 2687265, 7623504, 19482288, 45331650, 99729630, 207320256, 395793216, 694879416, 1158132360, 1835136576, 2682122688, 3618111196, 4651857252, 5702931360

A151771 Weight distribution of [63,39,9] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 2170, 11718, 32382, 140322, 628866, 2245950, 7302603, 21907809, 60355638, 154242186, 365056650, 803124630, 1648195230, 3146554530, 5596735032, 9327891720, 14579965764, 21309180732

A151772 Weight distribution of [63,45,7] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 3411, 23877, 78400, 423360, 2388456, 10349976, 39912768, 142545600, 465744279, 1397232837, 3864176064, 9875116608, 23391438840, 51461165448, 105345653952, 201114430272, 358601331375, 597668885625

A151773 Weight distribution of [63,51,5] primitive binary BCH code.

1, 0, 0, 0, 0, 1890, 18270, 133443, 934101, 5789350, 31262490, 150280200, 651214200, 2556010044, 9128607300, 29816643927, 89449931781, 247309297956, 632012650332, 1496867946840, 3293109483048

A151810 Weight distribution of [127,15,55] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3556, 4572, 0, 0, 0, 0, 0, 0, 8255, 8255, 0, 0, 0, 0, 0, 0, 4572, 3556, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

A151811 Weight distribution of [127,22,47] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16002, 26670, 0, 0, 0, 0, 0, 0, 384048, 493776, 0, 0, 0, 0, 0, 0, 1176655, 1176655, 0, 0, 0, 0, 0, 0, 493776, 384048, 0, 0, 0, 0, 0, 0

A151812 Weight distribution of [127,29,43] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128524, 245364, 0, 0, 954786, 1591310, 0, 0, 6518148, 9526524, 0, 0, 24678640, 31729680, 0, 0, 54726840, 62023752, 0, 0, 76311887

A151813 Weight distribution of [127,36,31] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2667, 8001, 0, 0, 4572, 11684, 0, 0, 640080, 1408176, 0, 0, 12220956, 23330916, 0, 0, 132560568, 220934280, 0, 0, 823921644, 1204193172, 0, 0, 3157059472

A151815 Weight distribution of [127,43,31] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31115, 93345, 0, 0, 2478024, 6332728, 0, 0, 82356960, 181185312, 0, 0, 1554145736, 2967005496, 0, 0, 16837453752, 28062422920, 0, 0, 106485735720

A151818 Weight distribution of [127,64,21] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41910, 201930, 1285494, 5570474, 21935186, 86053422, 323695568, 1156055600, 3886222860, 12694994676, 40367970699, 121103912097, 343251594420, 948989702220

A151838 Weight distribution of [127,71,19] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 417830, 2256282, 6442964, 31043372, 157443678, 682255938, 2808212316, 11016832932, 41125294686, 146876052450, 501584808360, 1638510373976, 5127674481867

A151839 Weight distribution of [127,78,15] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48387, 338709, 768096, 4693920, 33284160, 179734464, 912632160, 4397227680, 20128275720, 87222528120, 358733348064, 1407338519328, 5266329775168, 18808320625600

A151840 Weight distribution of [127,85,13] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37338, 304038, 2765171, 19356197, 120511062, 736456490, 4254825120, 22976055648, 116946815128, 563471018344, 2572832433192, 11148940543832, 45932301765896, 180195953081592

A151841 Weight distribution of [127,92,11] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112014, 1082802, 4992624, 40654224, 343960323, 2407722261, 15478798608, 94592658160, 544439184170, 2939971594518, 14970193795392, 72129115559616, 329317484468616, 1427042432697336

A151876 Weight distribution of [127,106,7] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 48387, 725805, 8249920, 97349056, 1065157128, 10296518904, 90631060800, 737995780800, 5564376646815, 38950636527705, 254287368764352, 1553978364671040, 8915151283570840

A151877 Weight distribution of [127,113,5] primitive binary BCH code.

1, 0, 0, 0, 0, 16002, 325374, 5455539, 81833085, 1081441830, 12761013594, 135766920744, 1312413567192, 11609278871820, 94532699384820, 712151423629407, 4985059965405849, 32549472610146324

A151878 Weight distribution of [255,37,91] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 563040, 1003680, 0, 0, 2754306, 4590510, 0, 0, 22848000, 35642880, 0, 0, 125386560, 183257280, 0, 0, 501228000, 686868000

A151909 Weight distribution of [255,45,87] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10875920, 20763120, 0, 0, 85112880, 151722960, 0, 0, 839823426, 1399705710, 0, 0, 5839330000, 9109354800

A151933 Weight distribution of [255,47,85] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8927058, 17646510, 10875920, 20763120, 73352790, 135295146, 85112880, 151722960

A151934 Weight distribution of [255,55,63] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10795, 32385, 35700, 94860, 293760, 750720, 3102840, 7080840, 7221600, 15887520

A151935 Weight distribution of [255,63,63] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10795, 32385, 67320, 193800, 410550, 1090890, 2074680, 5301960, 28493700

A151936 Weight distribution of [255,207,13] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8721510, 150757530, 2251459107, 33771886605, 472011374250, 6241039281750, 77847220528800, 918597202239840, 10278084342056520, 109321442547328440, 1107488282649954120

A151937 Weight distribution of [255,215,11] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7152750, 145439250, 2134260240, 36892212720, 575741656947, 8636124854205, 120888835017840, 1598419040791440, 19927324013927850, 235142423364348630, 2631224344379928000

A151938 Weight distribution of [255,223,9] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 2586550, 63629130, 1389956550, 28262449850, 528075710190, 9128165847570, 146665445085747, 2199981676286205, 30929084994308490, 408951234924745590, 5101129401023536050

A151939 Weight distribution of [255,231,7] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 856035, 26537085, 645102400, 15869519040, 355776960840, 7234131537080, 135192235752000, 2336894360856000, 37546273785247407, 563194106778711105, 7917846995071200960, 104691532490385879360

A151940 Weight distribution of [255,239,5] primitive binary BCH code.

1, 0, 0, 0, 0, 134946, 5622750, 195214995, 6051664845, 166197204550, 4088451231930, 91058768160360, 1851528285927320, 34609373477200620, 598247741534467860, 9611846516874799215, 144177697753121988225

A030639 Weight distribution of [128,43,32] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 124460, 8810752, 263542272, 4521151232, 44899876672, 262118734080, 915924097536, 1931974003456, 2476672341286, 1931974003456, 915924097536, 262118734080, 44899876672, 4521151232

A147628 Weight distribution of [64,10,28] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 448, 126, 448, 0, 0, 0, 0, 0, 0, 1

A147632 Weight distribution of [64,16,24] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 5040, 12544, 30366, 12544, 5040, 0, 0, 0, 0, 0, 1

A147633 Weight distribution of [128,15,56] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 8128, 16510, 8128, 0, 0, 0, 0, 0, 0, 1

A147635 Weight distribution of [128,22,48] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 42672, 877824, 2353310, 877824, 42672, 0, 0, 0, 0, 0, 1

A109488 Weight distribution of [64,18,22] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4224, 5040, 24192, 12544, 69888, 30366, 69888, 12544, 24192, 5040, 4224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A147770 Weight distribution of [128,29,44] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 373888, 2546096, 16044672, 56408320, 116750592, 152623774, 116750592, 56408320, 16044672, 2546096, 373888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151411 Weight distribution of [128,36,32] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 10668, 16256, 2048256, 35551872, 353494848, 2028114816, 7216135936, 14981968512, 19484794406, 14981968512, 7216135936, 2028114816, 353494848, 35551872, 2048256, 16256, 10668, 0, 0, 0, 0, 0, 0, 0, 1

A140792 Weight distribution of [128,64,22] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243840, 6855968, 107988608, 1479751168, 16581217536, 161471882796, 1292241296640, 9106516329984, 53383279307904, 278420690161824, 1218666847725184, 4782630191822848

A151422 Weight distribution of [128,50,28] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 186944, 19412204, 1103839296, 33723852288, 579267441920, 5744521082944, 33558415333632, 117224663972352, 247312085243776, 316992306111910, 247312085243776, 117224663972352, 33558415333632

A151435 Weight distribution of [128,57,24] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 597408, 24579072, 2437776684, 141621881856, 4315318568736, 74150180302848, 735289205007168, 4295496356229120, 15004724612905792, 31655991621445632, 40574965317267238, 31655991621445632

A151513 Weight distribution of [128,71,20] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2674112, 37486336, 839699616, 13825045248, 188001347136, 2140095182336, 20510697927468, 166689980438016, 1156658661471040, 6886497209935616, 35363776220195360

A151559 Weight distribution of [128,85,14] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 341376, 22121368, 856967552, 27230880768, 680417833472, 13721772977024, 226128254847488, 3081454360189952, 35064826913355520, 336014520825141340, 2731238665152128768, 18949612280501341184

A151560 Weight distribution of [128,92,12] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 1194816, 45646848, 2751682584, 110071456768, 3484410778688, 87099309355008, 1756359917165952, 28944450656120832, 394426389988237184, 4488297727663171584, 43009842715896693084

A151561 Weight distribution of [128,99,10] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 796544, 90180160, 6463889536, 347764539928, 14127559573120, 445754705469248, 11149685265467776, 224811690627712384, 3704895377802191104, 50486556173121673600, 574502176730571255552

A151562 Weight distribution of [128,106,8] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 774192, 105598976, 11361676032, 828626841600, 44515013174520, 1808265733435392, 57056968214853376, 1427159096213901312, 28775892186952836240, 474226642406696116224, 6462279071735110418944

A151563 Weight distribution of [128,113,6] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 341376, 87288624, 13842455424, 1448180487936, 106141978256640, 5697211389035256, 231462916338818304, 7303265469631124224, 182676478544670888576, 3683313800412335283600

A151564 Weight distribution of [256,13,120] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3840, 510, 3840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151618 Weight distribution of [256,21,112] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168640, 373760, 1012350, 373760, 168640, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151619 Weight distribution of [256,29,96] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 359856, 37361920, 113229824, 234967710, 113229824, 37361920, 359856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151620 Weight distribution of [256,37,92] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1566720, 7344816, 58490880, 308643840, 1188096000, 3727770880, 8903669760, 16687560704, 24073697280, 27525271710, 24073697280, 16687560704, 8903669760

A151621 Weight distribution of [256,45,88] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31639040, 236835840, 2239529136, 14948684800, 77258749440, 307810693120, 951255133440, 2282992005120, 4259254518784, 6189970585600, 7012375340190

A151622 Weight distribution of [256,47,86] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26573568, 31639040, 208647936, 236835840, 2378672640, 2239529136, 17829665280, 14948684800, 105426881280

A151623 Weight distribution of [256,55,64] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43180, 0, 0, 130560, 1044480, 10183680, 23109120, 270781440, 319610880, 4518816768, 5955102720, 59945135616, 64479928320, 598790983680

A151660 Weight distribution of [256,63,64] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43180, 261120, 0, 1501440, 7376640, 98572800, 172078080, 2851952640, 4852262400, 67242055680, 96309150720, 1166182422528, 1459521557760

A151695 Weight distribution of [256,207,14] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 159479040, 36023345712, 6713050656000, 996444422768640, 119599526889384960, 11813208348266177280, 973987499253055749120, 67857073021007558686720, 4036793565003066065373696

A151696 Weight distribution of [256,215,12] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 152592000, 39026472960, 9211866511152, 1719307875809280, 255069747378276480, 30617883280057344000, 3024174483076543522560, 249340897041415947755520, 17371409537486044559307520

A151697 Weight distribution of [256,223,10] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 66215680, 29652406400, 9656241557760, 2346647121371952, 439880319919054080, 65294456333101261440, 7838161222769040003840, 774188816874234585880320, 63831272413784249623288320

A151698 Weight distribution of [256,231,8] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 27393120, 16514621440, 7589908497920, 2472086596608000, 600740380563958512, 112609379485457080320, 16715380562421902753280, 2006569275819918529044480, 198192337104269951401589280

A151699 Weight distribution of [256,239,6] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 5757696, 6246879840, 4254648436480, 1942587054087680, 632857115011668480, 153789544269996787440, 28828000933861770693120, 4279137422192146077365760, 513681734709283283653090560
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