Hasse-Weil bound for additive cyclic codes

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Guneri C., ÖZBUDAK F., Ozdemir F.

DESIGNS CODES AND CRYPTOGRAPHY, vol.82, pp.249-263, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 82
  • Publication Date: 2017
  • Doi Number: 10.1007/s10623-016-0198-3
  • Journal Name: DESIGNS CODES AND CRYPTOGRAPHY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.249-263
  • Keywords: Additive cyclic code, Algebraic curve over a finite field, Hasse-Weil bound, BCH bound
  • Middle East Technical University Affiliated: Yes

Abstract

We obtain a bound on the minimum distance of additive cyclic codes via the number of rational points on certain algebraic curves over finite fields. This is an extension of the analogous bound in the case of classical cyclic codes. Our result is the only general bound on such codes aside from Bierbrauer's BCH bound. We compare our bounds' performance against the BCH bound for additive cyclic codes in a special case and provide examples where it yields better results.