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- Title
CYCLIC AND BCH CODES WHOSE MINIMUM DISTANCE EQUALS THEIR MAXIMUM BCH BOUND.
- Authors
BERNAL, JOSÉ JOAQUÍN; BUENO-CARREÑO, DIANA H.; SIMÓN, JUAN JACOBO
- Abstract
In this paper we study the family of cyclic codes such that its minimum distance reaches the maximum of its BCH bounds. We also show a way to construct cyclic codes with that property by means of computations of some divisors of a polynomial of the form xn – 1. We apply our results to the study of those BCH codes C, with designed distance δ, that have minimum distance d(C) = δ. Finally, we present some examples of new binary BCH codes satisfying that condition. To do this, we make use of two related tools: the discrete Fourier transform and the notion of apparent distance of a code, originally defined for multivariate abelian codes.
- Subjects
BCH codes; ANGULAR distance; FOURIER transforms; DIVISOR theory; BINARY codes
- Publication
Advances in Mathematics of Communications, 2016, Vol 10, Issue 2, p459
- ISSN
1930-5346
- Publication type
Article
- DOI
10.3934/amc.2016018