Cocyclic Development of Designs
Journal of Algebraic Combinatorics: An International Journal
An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A genetic algorithm for cocyclic hadamard matrices
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A mathematica notebook for computing the homology of iterated products of groups
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Rooted Trees Searching for Cocyclic Hadamard Matrices over D4t
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A heuristic procedure with guided reproduction for constructing cocyclic Hadamard matrices
ICANNGA'09 Proceedings of the 9th international conference on Adaptive and natural computing algorithms
Hadamard matrices and their applications: Progress 2007---2010
Cryptography and Communications
On an inequivalence criterion for cocyclic Hadamard matrices
Cryptography and Communications
ACS searching for D4t-Hadamard matrices
ANTS'10 Proceedings of the 7th international conference on Swarm intelligence
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An alternate method for constructing (Hadamard) cocyclic matrices over a finite group G is described. Provided that a homological model for G is known, the homological reduction method automatically generates a full basis for 2-cocycles over G (including 2-coboundaries). From these data, either an exhaustive or a heuristic search for Hadamard cocyclic matrices is then developed. The knowledge of an explicit basis for 2-cocycles which includes 2-coboundaries is a key point for the designing of the heuristic search. It is worth noting that some Hadamard cocyclic matrices have been obtained over groups G for which the exhaustive searching techniques are not feasible. From the computational-cost point of view, even in the case that the calculation of such a homological model is also included, comparison with other methods in the literature shows that the homological reduction method drastically reduces the required computing time of the operations involved, so that even exhaustive searches succeeded at orders for which previous calculations could not be completed. With aid of an implementation of the method in MATHEMATICA, some examples are discussed, including the case of very well-known groups (finite abelian groups, dihedral groups) for clarity.