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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.

An algorithm for calculating a set of generators of representative 2-cocycles on semidirect product of finite abelian groups is constructed, in light of the theory over cocyclic matrices developed by Horadam and de Launey in [7, 8]. The method involves some homological perturbation techniques [3, 1], in the homological correspondent to the work which… (More)

- Víctor Álvarez, José Ándrés Armario, María Dolores Frau, Pedro Real Jurado
- J. Symb. Comput.
- 2009

Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGA-algebra) and X be a relatively free resolution of Λ over A. The standard bar resolution of Λ over A, denoted by B(A), provides an example of a resolution of this kind. The comparison theorem gives inductive formulae f :B(A)→ X and g:X → B(A) termed comparison maps.… (More)

We describe a notebook in Mathematica which, taking as input data a homological model for a finite group G of order |G| = 4t, performs an exhaustive search for constructing the whole set of cocyclic Hadamard matrices over G. Since such an exhaustive search is not practical for orders 4t ≥ 28, the program also provides an alternate method, in which an… (More)

Let G be a group which admits the structure of an iterated product of central extensions and semidirect products of abelian groups Gi (both finite and infinite). We describe a Mathematica 4.0 notebook for computing the homology of G, in terms of some homological models for the factor groups Gi and the products involved. Computational results provided by our… (More)

- Víctor Álvarez, María Dolores Frau, Amparo Osuna
- ICANNGA
- 2009

- Víctor Álvarez, José Ándrés Armario, +4 authors Amparo Osuna
- ArXiv
- 2012

A genetic algorithm based robust blind digital watermarking scheme is presented. Starting from a binary image (the original watermark), a genetic algorithm is performed searching for a permutation of this image which is as uncorrelated as possible to the original watermark. The output of the GA is used as our final watermark, so that both security and… (More)