Families of nested completely regular codes and distance-regular graphs

Joaquim Borges, Josep Rifà, Victor A. Zinoviev

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

© 2015 AIMS. In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ∈ equal to 3 or 4; and are 1=2ith parts, for i ϵ {1,…,u} of binary (respectively, extended binary) Hamming codes of length n = 2m–1 (respectively, 2m), 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. This gives antipodal covers of some distance-regular and distance-transitive graphs. In some cases, the constructed codes are also completely transitive and the corresponding coset graphs are distance-transitive.
Original languageEnglish
Pages (from-to)233-246
JournalAdvances in Mathematics of Communications
Volume9
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Completely regular codes
  • Completely transitive codes
  • Distance-regular graphs
  • Distance-transitive graphs

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