Designs, Codes and Cryptography

, Volume 82, Issue 1–2, pp 249–263 | Cite as

Hasse–Weil bound for additive cyclic codes

Article

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.

Keywords

Additive cyclic code Algebraic curve over a finite field Hasse–Weil bound BCH bound 

Mathematics Subject Classification

94B27 94B65 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Faculty of Engineering and Natural SciencesSabancı UniversityIstanbulTurkey
  2. 2.Department of Mathematics and Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

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