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artemjackson/hemming.m

Last active June 2, 2016 16:23
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Hemming Matrix
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hemming.m
Needs["FiniteFields`"];
MultiplicativeGroupOfPolynomial[p_, g_, l_] :=
Block[{polynomial = p, generating = g, limit = l},
DeleteDuplicates@NestList[PolynomialMod[(generating*#), {polynomial, 2}] &, 1, limit]
];
BinaryForm[p_, d_] :=
Block[{polynomial = p, dimension = d},
Reverse@CoefficientList[polynomial, \[Alpha], dimension]
];
HemmingMatrix[n_, m_] :=
Block[{irreducablePolynomial, generating},
irreducablePolynomial = IrreduciblePolynomial[\[Alpha], 2, m];
generating = PolynomialMod[\[Alpha]^((2^m - 1)/n), {irreducablePolynomial, 2}];
Transpose[BinaryForm[#, m] & /@ MultiplicativeGroupOfPolynomial[irreducablePolynomial, generating, n]]
];
HemmingMatrix[103, 51]
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