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

4, 10, 24, 46, 72, 260, 400, 766, 1584, 2900, 4104, 19596, 16392, 67240, 139968, 196606, 266256, 1098760, 1048584, 3416604, 10454400, 10506260, 16810000, 83667116, 75497616, 167854100, 415239264, 1275614776, 1073741832, 6341140000, 6179217664, 12884901886

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..32.

Formula

See A143695 for formula.

Prog

(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 */
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

Crossrefs

Cf. A143695.

Sequence in context: A008251 A174934 A083168 * A058514 A182094 A291949

Adjacent sequences: A143693 A143694 A143695 * A143697 A143698 A143699

Keyword

nonn

Author

N. J. A. Sloane, Nov 13 2008, based on email from W. C. Huffman

Extensions

More terms from Michel Marcus, Mar 06 2013

Status

approved