Construction of self dual codes from graphs

Fellah N., Guenda K., ÖZBUDAK F., Seneviratne P.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol.35, no.4, pp.545-556, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.1007/s00200-022-00567-2
  • Journal Name: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.545-556
  • Keywords: Paley-type bipartite graphs, Hadamard matrices, Self-dual codes, Extremal doubly even codes, MATRICES
  • Middle East Technical University Affiliated: Yes

Abstract

In this work we define and study binary codes C-q,C-k and (C-q,C-k) over bar obtained from neighbor- hood designs of Paley-type bipartite graphs P(q, k) and their complements, respectively for q an odd prime. We prove that for some values of q and k the codes C-q,C-k are self-dual and the codes (C-q,C-k) over bar are self-orthogonal. Most of these codes tend to be with optimal or near optimal parameters. Next, we extend the codes C(q,k )to get doubly even self dual codes and find that most of these codes are extremal.