Hasse-Weil bound for additive cyclic codes

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Guneri C., ÖZBUDAK F., Ozdemir F.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 82
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s10623-016-0198-3
  • Dergi Adı: DESIGNS CODES AND CRYPTOGRAPHY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.249-263
  • Anahtar Kelimeler: Additive cyclic code, Algebraic curve over a finite field, Hasse-Weil bound, BCH bound
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.