Completely regular codes with different parameters giving the same distance-regular coset graphs

J. Rifà, V. A. Zinoviev

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

© 2017 Elsevier B.V. We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min{a,b} and identical intersection array, specifically, one code over Fqr for each divisor r of a or b. As a corollary, for any prime power q, we show that distance regular bilinear forms graphs can be obtained as coset graphs from several completely regular codes with different parameters.
Original languageEnglish
Pages (from-to)1649-1656
JournalDiscrete Mathematics
Volume340
Issue number7
DOIs
Publication statusPublished - 1 Jul 2017

Keywords

  • Bilinear forms graph
  • Completely regular code
  • Completely transitive code
  • Coset graph
  • Distance-regular graph
  • Distance-transitive graph
  • Kronecker product construction
  • Lifting of a field
  • Uniformly packed code

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