A Genetic Algorithm for Cocyclic Hadamard Matrices

A genetic algorithm for finding cocyclic Hadamard matrices is described. Though we focus on the case of dihedral groups, the algorithm may be easily extended to cover any group. Some executions and examples are also included, with aid of Mathematica 4.0.

[1]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[2]  V. K. A. M. Gugenheim,et al.  Perturbation Theory in Dierential Homological Algebra II , 1989 .

[3]  A. Baliga,et al.  Self-dual Codes Using Image Restoration Techniques , 2001, AAECC.

[4]  D. Flannery,et al.  Cocyclic Hadamard Matrices and Hadamard Groups Are Equivalent , 1997 .

[5]  A. L.,et al.  PERTURBATION THEORY IN DIFFERENTIAL HOMOLOGICAL ALGEBRA I , 2022 .

[6]  Larry A. Lambe,et al.  Computing Resolutions Over Finite p-Groups , 2001 .

[7]  Víctor Álvarez,et al.  An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products , 2001, AAECC.

[8]  K. J. Horadam,et al.  Cocyclic Development of Designs , 1993 .

[9]  Pedro Real,et al.  Homological perturbation theory and associativity , 2000 .

[10]  E. O'Brien,et al.  Computing 2-cocyeles for central extensions and relative difference sets , 2000 .

[11]  K. J. Horadam,et al.  Generation of Cocyclic Hadamard Matrices , 1995 .

[12]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[13]  Kathy J. Horadam,et al.  Cocyclic Hadamard matrices over ℤt × ℤ22 , 1995, Australas. J Comb..

[14]  D. Flannery,et al.  Calculation of cocyclic matrices , 1996 .

[15]  Zbigniew Michalewicz,et al.  Genetic Algorithms Plus Data Structures Equals Evolution Programs , 1994 .

[16]  V. K. A. M. Gugenheim,et al.  Perturbation Theory in Dierential Homological Algebra II , 1989 .