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A143695
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Number of additive cyclic codes over GF(4) of length n.
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1
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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
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OFFSET
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1,1
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REFERENCES
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W. C. Huffman, Additive cyclic codes over F_4, Advances in Math. Communication, 2 (2008), 309-343.
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LINKS
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FORMULA
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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).
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PROG
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(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))); }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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