Abstract
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.
All authors are partially supported by the PAICYT research project FQM–296 from Junta de Andalucía (Spain).
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References
Álvarez, V., Armario, J.A., Frau, M.D., Real, P.: An algorithm for computing cocyclic matrices developed over some semidirect products. In: Bozta, S., Sphparlinski, I. (eds.) AAECC 2001. LNCS, vol. 2227, p. 287. Springer, Heidelberg (2001)
Álvarez, V., Armario, J.A., Frau, M.D., Real, P.: Homological reduction method for constructing cocyclic Hadamard matrices (to appear)
Álvarez, V., Armario, J.A., Frau, M.D., Real, P.: How to bound the search space looking for cocyclic Hadamard matrices (to appear)
Baliga, A., Chua, J.: Self-dual codes using image resoration techniques. In: Bozta, S., Sphparlinski, I. (eds.) AAECC 2001. LNCS, vol. 2227, p. 46. Springer, Heidelberg (2001)
Baliga, A., Horadam, K.J.: Cocyclic Hadamard matrices over ℤ t × ℤ2. Australas. J. Combin. 11, 123–134 (1995)
de Launey, W., Horadam, K.J.: Cocyclic development of designs. J. Algebraic Combin. 2(3), 267–290 (1993); Erratum: J. Algebraic Combin. (1), 129 (1994)
de Launey, W., Horadam, K.J.: Generation of cocyclic Hadamard matrices. In: Computational algebra and number theory Sydney 1992. Math. Appl., vol. 325, pp. 279–290. Kluwer Acad. Publ., Dordrecht (1995)
Flannery, D.L.: Calculation of cocyclic matrices. J. of Pure and Applied Algebra 112, 181–190 (1996)
Flannery, D.L.: Cocyclic Hadamard matrices and Hadamard groups are equivalent. J. Algebra 192, 749–779 (1997)
Flannery, D.L., O’Brien, E.A.: Computing 2-cocycles for central extensions and relative difference sets. Comm. Algebra 28(4), 1939–1955 (2000)
Grabmeier, J., Lambe, L.A.: Computing Resolutions Over Finite p-Groups. In: Betten, A., Kohnert, A., Lave, R., Wassermann, A. (eds.) Proceedings ALCOMA 1999. Springer Lecture Notes in Computational Science and Engineering. Springer, Heidelberg (2000)
Gugenheim, V.K.A.M., Lambe, L.A.: Perturbation theory in Differential Homological Algebra, I. Illinois J. Math. 33, 556–582 (1989)
Gugenheim, V.K.A.M., Lambe, L.A., Stasheff, J.D.: Perturbation theory in Differential Homological Algebra II. Illinois J. Math. 35(3), 357–373 (1991)
Holland, J.H.: Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor (1975)
Michalewicz, Z.: Genetic algorithms + data structures = evolution programs. Springer, Heidelberg (1992)
Real, P.: Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications 2, 51–88 (2000)
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Álvarez, V., Armario, J.A., Frau, M.D., Real, P. (2006). A Genetic Algorithm for Cocyclic Hadamard Matrices. In: Fossorier, M.P.C., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2006. Lecture Notes in Computer Science, vol 3857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11617983_14
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DOI: https://doi.org/10.1007/11617983_14
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