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Designs, Codes and Cryptography

, Volume 70, Issue 1–2, pp 139–148 | Cite as

New families of completely regular codes and their corresponding distance regular coset graphs

  • Joaquim Borges
  • Josep Rifà
  • Victor Zinoviev
Article

Abstract

In this paper three new infinite families of linear binary completely regular codes are constructed. They have covering radius ρ = 3 and 4, and are halves of binary Hamming and binary extended Hamming codes of length n = 2 m −1 and 2 m , where m is even. There are also shown some combinatorial (binomial) identities which are new, to our knowledge.These completely regular codes induce, in the usual way, i.e., as coset graphs, three infinite families of distance-regular graphs of diameter three and four. This description of such graphs is new.

Keywords

Completely regular codes Distance regular graphs t-Designs 

Mathematics Subject Classification

94B25 94B60 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Information and Communications EngineeringUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Institute for Problems of Information TransmissionRussian Academy of SciencesMoscowRussia

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