SELF-DUALITY OF GENERALIZED TWISTED GABIDULIN CODES


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Otal K. , ÖZBUDAK F. , Willems W.

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol.12, no.4, pp.707-721, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.3934/amc.2018042
  • Title of Journal : ADVANCES IN MATHEMATICS OF COMMUNICATIONS
  • Page Numbers: pp.707-721
  • Keywords: Rank metric codes, self-dual maximum rank distance codes, generalized twisted Gabidulin codes, linearized polynomials

Abstract

Self-duality of Gabidulin codes was investigated in [10]and the authors provided an if and only if condition for a Gabidulin code to be equivalent to a self-dual maximum rank distance (MRD) code. In this paper, we investigate the analog problem for generalized twisted Gabidulin codes (a larger family of linear MRD codes including the family of Gabidulin codes). We observe that the condition presented in [10] still holds for generalized Gabidulin codes (an intermediate family between Gabidulin codes and generalized twisted Gabidulin codes). However, beyond the family of generalized Gabidulin codes we observe that some additional conditions are required depending on the additional parameters. Our tools are similar to those in [10] but we also use linearized polynomials, which leads to further tools and direct proofs.