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Apparent Distance and a Notion of BCH Multivariate Codes
- Source :
- IEEE Transactions on Information Theory. 62:655-668
- Publication Year :
- 2016
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2016.
-
Abstract
- This paper is devoted to studying two main problems: 1) computing the apparent distance of an Abelian code and 2) giving a notion of Bose, Ray-Chaudhuri, Hocquenghem (BCH) multivariate code. To do this, we first strengthen the notion of an apparent distance by introducing the notion of a strong apparent distance; then, we present an algorithm to compute the strong apparent distance of an Abelian code, based on some manipulations of hypermatrices associated with its generating idempotent. Our method uses less computations than those given by Camion and Sabin; furthermore, in the bivariate case, the order of computation complexity is reduced from exponential to linear. Then, we use our techniques to develop a notion of a BCH code in the multivariate case, and we extend most of the classical results on cyclic BCH codes. Finally, we apply our method to the design of Abelian codes with maximum dimension with respect to a fixed apparent distance and a fixed length.
- Subjects :
- Discrete mathematics
Polynomial code
Concatenated error correction code
020206 networking & telecommunications
0102 computer and information sciences
02 engineering and technology
Library and Information Sciences
01 natural sciences
MAXEkSAT
Linear code
Computer Science Applications
Combinatorics
010201 computation theory & mathematics
Group code
Reed–Solomon error correction
0202 electrical engineering, electronic engineering, information engineering
Low-density parity-check code
BCH code
Information Systems
Mathematics
Subjects
Details
- ISSN :
- 15579654 and 00189448
- Volume :
- 62
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Information Theory
- Accession number :
- edsair.doi...........f302b91e594ebae43be52df83b495904