A new shortening method and Hermitian self-dual codes over F-2 + vF(2)

Aksoy R., ÇALIŞKAN F.

DISCRETE MATHEMATICS, vol.343, no.7, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 343 Issue: 7
  • Publication Date: 2020
  • Doi Number: 10.1016/j.disc.2019.111716
  • Journal Name: DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, MathSciNet, zbMATH
  • Istanbul University Affiliated: Yes

Abstract

In this paper, we investigate free Hermitian self-dual codes whose generator matrices are of the form [I, A + vB] over the ring F-2 + vF(2) = {0, 1, v, 1 + v} with v(2) = v. We use the double-circulant, the bordered double-circulant and the symmetric construction methods to obtain free Hermitian self-dual codes of even length. By describing a new shortening method over this ring, we are able to obtain Hermitian self-dual codes of odd length. Using these methods, we also obtain a number of extremal codes. We tabulate the Hermitian self-dual codes with the highest minimum weights of lengths up to 50. (C) 2019 Elsevier B.V. All rights reserved.