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 A143696 Number of additive cyclic codes over GF(4) of length n that can be generated by one codeword. 1

%I #12 Jun 14 2022 07:01:26

%S 4,10,24,46,72,260,400,766,1584,2900,4104,19596,16392,67240,139968,

%T 196606,266256,1098760,1048584,3416604,10454400,10506260,16810000,

%U 83667116,75497616,167854100,415239264,1275614776,1073741832,6341140000,6179217664,12884901886

%N Number of additive cyclic codes over GF(4) of length n that can be generated by one codeword.

%D W. C. Huffman, Additive cyclic codes over F_4, Advances in Math. Communication, 2 (2008), 309-343.

%F See A143695 for formula.

%o (PARI) csiz(n, q) = {list = listcreate(n); A = vector(n); for (i=0, n-1, ai = i+1; if (!A[ai], ni = i; nai = ni+1; s = 0; while (! A[nai], A[nai] = 1; s++; ni = lift(Mod(ni*q, n)); nai = ni+1; ); listput(list, s); ); ); return (Vec(list)); } /* algorithm from arXiv:cs/0703129 */

%o a(n) = {expz = 2^valuation(n, 2); y = n/expz; d = csiz(y, 2); prod(i=1, length(d), 1 + (2^(expz*d[i])-1)*(2^d[i]+1)/(2^d[i]-1));} \\ _Michel Marcus_, Mar 06 2013

%Y Cf. A143695.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Nov 13 2008, based on email from W. C. Huffman

%E More terms from _Michel Marcus_, Mar 06 2013

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Last modified September 27 04:27 EDT 2023. Contains 365672 sequences. (Running on oeis4.)