Efficient representation of binary nonlinear codes : constructions and minimum distance computation
Villanueva, M. (Mercè) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Pujol Capdevila, Jaume (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Zeng, Fanxuan (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)

Date:	2015
Abstract:	A binary nonlinear code can be represented as a union of cosets of a binary linear subcode. In this paper, the complexity of some algorithms to obtain this representation is analyzed. Moreover, some properties and constructions of new codes from given ones in terms of this representation are described. Algorithms to compute the minimum distance of binary nonlinear codes, based on known algorithms for linear codes, are also established, along with an algorithm to decode such codes. All results are written in such a way that they can be easily transformed into algorithms, and the performance of these algorithms is evaluated.
Grants:	Ministerio de Ciencia e Innovación TIN2013-40524-P Ministerio de Ciencia e Innovación TIN2010-17358 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-691
Note:	Combinatorics, Coding and Security Group (CCSG)
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Nonlinear code ; Kernel ; Minimum distance ; Minimum weight ; Decoding ; Algorithms
Published in:	Designs, codes and cryptography, Vol. 76, Issue 1 (July 2015) , p. 3-21, ISSN 1573-7586

DOI: 10.1007/s10623-014-0028-4

Post-print 18 p, 1.2 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Engineering > Combinatorics, Coding and Security Group (CCSG)
Articles > Research articles
Articles > Published articles