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Pàgina inicial > Articles > Articles publicats > Families of nested completely regular codes and distance-regular graphs |
Data: | 2015 |
Resum: | 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. |
Ajuts: | Ministerio de Ciencia e Innovación TIN2013-40524-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-691 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Completely regular codes ; Completely transitive codes ; Distance-regular graphs ; Distance-transitive graphs |
Publicat a: | Advances in mathematics of communications, Vol. 9 Issue 2 (May 2015) , p. 233-246, ISSN 1930-5338 |
Post-print 21 p, 3.7 MB |