Artículo
Gröbner bases and cocyclic Hadamard matrices
Autor/es | Álvarez Solano, Víctor
Armario Sampalo, José Andrés Falcón Ganfornina, Raúl Manuel Frau García, María Dolores Gudiel Rodríguez, Félix |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2018 |
Fecha de depósito | 2019-10-17 |
Publicado en |
|
Resumen | Hadamard ideals were introduced in 2006 as a set of nonlin-ear polynomial equations whose zeros are uniquely related toHadamard matrices with one or two circulant cores of a given or-der. Based on this idea, the cocyclic ... Hadamard ideals were introduced in 2006 as a set of nonlin-ear polynomial equations whose zeros are uniquely related toHadamard matrices with one or two circulant cores of a given or-der. Based on this idea, the cocyclic Hadamard test enables us todescribe a polynomial ideal that characterizes the set of cocyclicHadamard matrices over a fixed finite group Gof order 4t. Nev-ertheless, the complexity of the computation of the reduced Gröb-ner basis of this ideal is 2O(t2), which is excessive even for very small orders. In order to improve the efficiency of this polynomialmethod, we take advantage of some recent results on the innerstructure of a cocyclic matrix to describe an alternative polyno-mial ideal that also characterizes the aforementioned set of cocyclicHadamard matrices over G. The complexity of the computation de-creases in this way to 2O(t). Particularly, we design two specific procedures for looking for Zt×Z22-cocyclic Hadamard matrices and D4t-cocyclic Hadamard matrices, so that larger cocyclic Hadamard matrices (up to t≤39) are explicitly obtained. |
Identificador del proyecto | FQM-016 |
Cita | Álvarez Solano, V., Armario Sampalo, J.A., Falcón Ganfornina, R.M., Frau García, M.D. y Gudiel Rodríguez, F. (2018). Gröbner bases and cocyclic Hadamard matrices. Journal of Symbolic Computation, 89 (November-December 2018), 26-40. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
Gröbner bases and cocyclic ... | 614.2Kb | [PDF] | Ver/ | |