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Search: id:A158078
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| A158078 |
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Coefficients of Golay C_23 weight distribution polynomial: p(x)=1 + 253*x^7 + 506*x^8 + 1288*x^11 + 1288*x^12 + 506*x^15 + 253*x^16 + x^23. |
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| 1, 0, 0, 0, 0, 0, 0, -253, -506, 0, 0, -1288, -1288, 0, 64009, 255530, 255783, 0, 651728, 1955184, 1303456, -16194277, -95250682, -190373347, -127639236, -247330776, -1235350424, -1976691024, 3108480705, 31420912490, 92858107023
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OFFSET
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0,8
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COMMENT
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Factoring p(x) gives:
p(x)=(1 + x)^7*(1 - 7 x + 28 x^2 - 84 x^3 + 210 x^4 -
462 x^5 + 924 x^6 - 1463 x^7 + 1738 x^8
- 1463 x^9 + 924 x^10 - 462 x^11 + 210 x^12
- 84 x^13 + 28 x^14 - 7 x^15 + x^16;
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REFERENCES
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F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 69.
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FORMULA
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p(x)=1 + 253*x^7 + 506*x^8 + 1288*x^11 + 1288*x^12 + 506*x^15 + 253*x^16 + x^23;
Since p(x) is suymmetric:
a(n)=coefficients(1/p(x)).
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MATHEMATICA
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f[x_] = 1 + 253* x^7 + 506*x^8 + 1288*x^11 + 1288*x^12 + 506*x^15 + 253*x^16 + x^23;
g[x] = ExpandAll[x^23*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: A010331 A088851 A002289 this_sequence A157356 A070193 A054737
Adjacent sequences: A158075 A158076 A158077 this_sequence A158079 A158080 A158081
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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 12 2009
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