Self-dual codes and orthogonal matrices over large finite fields


Shi M., Sok L., Sole P., ÇALKAVUR S.

FINITE FIELDS AND THEIR APPLICATIONS, vol.54, pp.297-314, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54
  • Publication Date: 2018
  • Doi Number: 10.1016/j.ffa.2018.08.011
  • Journal Name: FINITE FIELDS AND THEIR APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.297-314
  • Keywords: Orthogonal matrices, Self-dual codes, Optimal codes, Almost MDS codes, MDS codes, PRIME FIELDS, CONSTRUCTIONS
  • Kocaeli University Affiliated: Yes

Abstract

In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, code extension and projection over a self-dual basis are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large finite fields are constructed. Moreover, over fifty MDS codes with new parameters are constructed. Comparisons with classical constructions are made. (C) 2018 Elsevier Inc. All rights reserved.