Some new non-additive maximum rank distance codes

Otal K., Ozbudak F.

FINITE FIELDS AND THEIR APPLICATIONS, vol.50, pp.293-303, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50
  • Publication Date: 2018
  • Doi Number: 10.1016/j.ffa.2017.12.003
  • Journal Name: FINITE FIELDS AND THEIR APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.293-303
  • Keywords: Rank metric codes, Maximum rank distance (MRD) codes, Additive generalized twisted, Gabidulin codes, Linearized polynomials
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, a construction of maximum rank distance (MRD) codes as a generalization of generalized Gabidulin codes is given. The family of the resulting codes is not covered properly by additive generalized twisted Gabidulin codes, and does not cover all twisted Gabidulin codes. When the basis field has more than two elements, this family includes also non-affine MRD codes, and such codes exist for all parameters. Therefore, these codes are the first non-additive MRD codes for most of the parameters. (C) 2017 Elsevier Inc. All rights reserved.