Error Correcting Codes from Quasi-Hadamard Matrices

Authors:
V. Álvarez;J. A. Armario;M. D. Frau;E. Martin;A. Osuna
Affiliations:
Dpto. Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n 41012 Sevilla, Spain;Dpto. Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n 41012 Sevilla, Spain;Dpto. Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n 41012 Sevilla, Spain;Dpto. Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n 41012 Sevilla, Spain;Dpto. Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n 41012 Sevilla, Spain
Venue:
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Year:
2007

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Abstract

Levenshtein described in [5] a method for constructing error correcting codes which meet the Plotkin bounds, provided suitable Hadamard matrices exist. Uncertainty about the existence of Hadamard matrices on all orders multiple of 4 is a source of difficulties for the practical application of this method. Here we extend the method to the case of quasi-Hadamard matrices. Since efficient algorithms for constructing quasi-Hadamard matrices are potentially available from the literature (e.g. [7]), good error correcting codes may be constructed in practise. We illustrate the method with some examples.