Partial permutation decoding for binary linear and Z4-linear Hadamard codes
Barrolleta, Roland David
Villanueva, M. (Mercè) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)

Date:	2017
Abstract:	In this paper, s-PD-sets of minimum size s + 1 for partial permutation decoding for the binary linear Hadamard code H_m of length 2^m , for all m ≥ 4 and 2 ≤ s ≤ floor(2^m/(1+m)) -1, are constructed. Moreover, recursive constructions to obtain s-PD-sets of size l ≥ s + 1 for H_{m+1} of length 2^(m+1), from an s-PD-set of the same size for H_m , are also described. These results are generalized to find s-PD-sets for the Z4 -linear Hadamard codes H_{γ,δ} of length 2^m , m = γ + 2δ − 1, which are binary Hadamard codes (not necessarily linear) obtained as the Gray map image of quaternary linear codes of type 2^γ 4^δ . Specifically, s-PD-sets of minimum size s + 1 for H_{γ,δ} , for all δ ≥ 3 and 2 ≤ s ≤ floor(2^(2δ−2)/δ)-1, are constructed and recursive constructions are described.
Grants:	Ministerio de Economía y Competitividad TIN2016-77918-P Ministerio de Economía y Competitividad MTM2015-69138-REDT Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-691
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Automorphism group ; Permutation decoding ; PD-set ; Hadamard code ; Z4-linear code
Published in:	Designs, codes and cryptography, 2017 , ISSN 1573-7586

DOI: 10.1007/s10623-017-0342-8

Post-print 20 p, 319.4 KB

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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
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