Construction of self dual codes from graphs

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

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, cilt.35, sa.4, ss.545-556, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 4
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s00200-022-00567-2
  • Dergi Adı: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.545-556
  • Anahtar Kelimeler: Paley-type bipartite graphs, Hadamard matrices, Self-dual codes, Extremal doubly even codes, MATRICES
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.