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Search: id:A157876
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| A157876 |
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Coefficients of Leech lattice x^23+1 modulo two factor: f(x)=1 + x^2 + x^4 + x^5 + x^6 + x^10 + x^11; g(x)=1/(x^11*f(1/x)). |
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+0
1
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| 1, -1, 1, -1, 1, -2, 2, -3, 4, -6, 9, -12, 17, -22, 30, -40, 54, -74, 100, -138, 188, -258, 352, -479, 653, -887, 1209, -1645, 2242, -3056, 4165, -5680, 7740, -10551, 14376, -19589, 26692, -36368, 49560, -67532, 92032, -125416, 170912, -232912, 317392
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OFFSET
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0,6
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COMMENT
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Mod[x^23+1 ,2]=(x+1)*f(x)*f1(x);
f1(x) is the Golay g_2(x) cyclic code polynomial.
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, pp. 231.
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FORMULA
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f(x)=1 + x^2 + x^4 + x^5 + x^6 + x^10 + x^11; g(x)=1/(x^11*f(1/x)).
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MATHEMATICA
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f[x_] = 1 + x^2 + x^4 + x^5 + x^6 + x^10 + x^11;
g[x] = ExpandAll[x^11*f[1/x]];
a = Table[SeriesCoefficient[ Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]
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CROSSREFS
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Sequence in context: A035561 A068106 A005856 this_sequence A107293 A001611 A039829
Adjacent sequences: A157873 A157874 A157875 this_sequence A157877 A157878 A157879
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 08 2009
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