Families of nested completely regular codes and distance-regular graphs
Borges, J. (Joaquim) (Joaquim) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Zinoviev, Victor (Harkevich Institute for Problems of Information Transmission)

Date:	2015
Abstract:	In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ρ equal to 3 or 4, and are 1/2 i th parts, for i ∈ {1, . . . , u} of binary (respectively, extended binary) Hamming codes of length n = 2 m − 1 (respectively, 2 m ), where m = 2u. In the usual way, i. e. , as coset graphs, infinite families of embedded distance-regular coset graphs of diameter D equal to 3 or 4 are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive. This gives antipodal covers of some distance-regular and distance-transitive graphs.
Grants:	Ministerio de Ciencia e Innovación TIN2013-40524-P 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:	Completely regular codes ; Completely transitive codes ; Distance-regular graphs ; Distance-transitive graphs
Published in:	Advances in mathematics of communications, Vol. 9 Issue 2 (May 2015) , p. 233-246, ISSN 1930-5338

Adreça alternativa: https://publons.com/publon/9675739/
DOI: 10.3934/amc.2015.9.233

Post-print 21 p, 3.7 MB

The record appears in these collections:
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