Publication: Apparent distance and a notion of BCH multivariate codes
Authors
Bernal Buitrago, José Joaquín ; Bueno Carreño, Diana H. ; Simón Pinero, Juan Jacobo
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Publisher
Institute of Electrical and Electronics Engineers
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DOI
https://doi.org/10.1109/TIT.2015.2512594
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info:eu-repo/semantics/article
Description
©2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
This document is the Accepted, version of a Published Work that appeared in final form in IEEE Transactions on Information Theory. To access the final edited and published work see https://doi.org/10.1109/TIT.2015.2512594
Abstract
This paper is devoted to study two main problems: on the one hand, to compute the apparent distance of an abelian code and
on the other hand, to give a notion of BCH multivariate code. To do this, we present an algorithm to compute the apparent distance
of an abelian code, based on some manipulations of hypermatrices associated to its generating idempotent. Our method uses less
computations than those given in [5] and [10]; furthermore, in the bivariate case, the order of the computations is reduced from
exponential to linear. Then we use our techniques to develop a notion of BCH code in the multivariate case and we extend most
of the classical results on BCH codes. Finally, we apply our method in two directions: we construct abelian codes from cyclic
codes, multiplying their dimension and preserving their apparent distance; and we design abelian codes with maximum dimension
with respect to a fixed apparent distance and a fixed length.
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Citation
IEEE Transactions on Information Theory, 62 (2), 2015: 655 - 668.
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