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