Covering Radius of Melas Codes


Shi M., Helleseth T., Özbudak F., Sole P.

IEEE Transactions on Information Theory, vol.68, no.7, pp.4354-4364, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 68 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.1109/tit.2022.3152092
  • Journal Name: IEEE Transactions on Information Theory
  • Journal Indexes: Science Citation Index Expanded
  • Page Numbers: pp.4354-4364
  • Keywords: Melas code, covering radius, finite fields

Abstract

IEEEWe prove that the covering radius of the Melas code M(m, q) of length n = qm - 1 over Fq is 2 if q > 3. We also prove that the covering radius of M(m, 3) is 3 is m ≥ 3, the covering radius of M(2, 3) is 4, and the covering radii of M(1, 2) and M(1, 3) are 1.