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HadamardSearch
Authors

Victor Alvarez Solano
Organization: University of Seville (Spain)
Department: Matematica Aplicada I
Jose Andres Armario-Sampalo
Organization: University of Seville (Spain)
Department: Matematica Aplicada I
Maria Dolores Frau-Garcia
Organization: University of Seville (Spain)
Department: Matematica Aplicada I
Pedro Real-Jurado
Organization: University of Seville (Spain)
Department: Matematica Aplicada I
Revision date

2006-11-08
Description

This is a tool for looking for cocyclic Hadamard matrices over a finite group G for which a homological model hG is known, as described by V.Alvarez, J.A.Armario, M.D.Frau and P.Real in "Calculating cocyclic Hadamard matrices in Mathematica: exhaustive and heuristic searches", ICMS-06, Castro Urdiales, Spain (2006). To appear in a special issue of LNCS.

Two searching methods are provided. The exhaustive one developes a full search among all 2-cocycles. The heuristic search consists in a genetic algorithm, described by V.Alvarez, J.A.Armario, M.D.Frau and P.Real in "A genetic algorithm for cocyclic Hadamard matrices", AAECC-16, Las Vegas, USA, LNCS 3857, 144--153 (2006).

Six input data are needed:

1. A matrix PR representing the group law on G. 2. A matrix M2 representing the differential d2 on hG_2. 3. A matrix M3 representing the differential d3 on hG_3. 4. A matrix F1 representing the projection from B_1(Z[G]) to hG_1. 5. A matrix F2 representing the projection from B_2(Z[G]) to hG_2. 6. 1 for developing an exhaustive search, anything else for developing a heuristic search.
Subjects

*Applied Mathematics > Numerical Methods
*Mathematics > Algebra > Group Theory
*Mathematics > Discrete Mathematics > Coding Theory
*Mathematics > Number Theory
*Mathematics > Topology
Keywords

Cocyclic Hadamard matrix, homological model, genetic algorithm
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HadamardSearch.m (14.6 KB) - Mathematica Package
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HadamardSearch.nb (502.6 KB) - Mathematica Notebook
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Readme-HadamardSearch.nb (474.2 KB) - Mathematica Notebook