F. Gudiel

activity

20112026

collaborators

8 papers

math.CO2026

Fundamentals of the cocyclic development of Hadamard matrices over loops

Raúl M. Falcón, Manuel González-Regadera, Félix Gudiel

This paper establishes a formal framework for the cocyclic development of Hadamard matrices over loops based on a novel cohomology theory with associativity obstructions. In this c…

math.CO2016

Gröbner bases and cocyclic Hadamard matrices

V. Álvarez, J. A. Armario, R. M. Falcón +2

Hadamard ideals were introduced in 2006 as a set of nonlinear polynomial equations whose zeros are uniquely related to Hadamard matrices with one or two circulant cores of a given…

math.CO2015

Equivalences of $Z_{t} \times Z_{2}^{2}$ -cocyclic Hadamard matrices

V. Alvarez, F. Gudiel, M. B. Guemes +2

One of the most promising structural approaches to resolving the Hadamard Conjecture uses the family of cocyclic matrices over $Z_{t} \times Z_{2}^{2}$ . Two types of…

math.CO2013

Determinants of $(- 1, 1)$ -matrices of the skew-symmetric type: a cocyclic approach

V. Álvarez, J. A. Armario, M. D. Frau +1

An $n$ by $n$ skew-symmetric type $(- 1, 1)$ -matrix $K = [k_{i, j}]$ has $1$ 's on the main diagonal and $\pm 1$ 's elsewhere with $k_{i, j} = - k_{j, i}$ . The largest possible determinant of…

math.CO2012

GA based robust blind digital watermarking

Víctor Álvarez, José-Andrés Armario, María-Dolores Frau +4

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 f…

math.CO2012

Embedding cocyclic D-optimal designs in cocyclic Hadamard matrices

Víctor Álvarez, José-Andrés Armario, María-Dolores Frau +1

In this paper a method for embedding cocyclic submatrices with ``large'' determinants of orders 2t in certain cocyclic Hadamard matrices of orders 4t is described (t an odd integer…