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 A143695 Number of additive cyclic codes over GF(4) of length n. 1
 5, 15, 35, 83, 95, 495, 605, 1515, 2345, 4635, 5135, 46895, 20495, 129735, 240065, 393179, 335405, 2125035, 1310735, 6575675, 19010915, 15774795, 21033005, 220627935, 99615005, 251842635, 614734715, 3004955987, 1342177295, 14604296355, 9191328125, 25769803707 (list; graph; refs; listen; history; text; internal format)
 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. Joseph Geraci, Frank Van Bussel, A theorem on the quantum evaluation of Weight Enumerators for a certain class of Cyclic Codes with a note on Cyclotomic cosets, arXiv:cs/0703129, 2007-2008. FORMULA Let n=2^z y where y is odd. Let d_0,d_1, ..., d_s be the sizes of the 2-cyclotomic cosets modulo y. Then a(n) = \prod_{i=0}^s \left(1+2^z+\left(\frac{2^{d_i}+1}{2^{d_i}-1}\right)\left(\frac{2^{2^z{d_i}}-1}{2^{d_i}-1}-2^z+2^{2^z{d_i}}-1\right)\right). Also A143696(n) = \prod_{i=0}^s \left(1+\left(\frac{2^{d_i}+1}{2^{d_i}-1}\right)(2^{2^z{d_i}}-1)\right). 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 + expz + ((2^d[i]+1)/(2^d[i]-1)*((2^(expz*d[i])-1)/(2^d[i]-1) - expz + 2^(expz*d[i])-1))); } \\ Michel Marcus, Mar 06 2013 CROSSREFS Cf. A143696. Sequence in context: A221140 A330911 A322048 * A019531 A321345 A145454 Adjacent sequences: A143692 A143693 A143694 * A143696 A143697 A143698 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

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Last modified September 30 21:59 EDT 2023. Contains 365812 sequences. (Running on oeis4.)