Weil-Serre Type Bounds for Cyclic Codes

GÜNERİ C., ÖZBUDAK F.

IEEE TRANSACTIONS ON INFORMATION THEORY, cilt.54, sa.12, ss.5381-5395, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 12
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1109/tit.2008.2006436
  • Dergi Adı: IEEE TRANSACTIONS ON INFORMATION THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.5381-5395
  • Anahtar Kelimeler: Additive polynomials, cyclic code, factorization left greatest common divisor, trace representation, Weil-Serre bound, WEIGHT DISTRIBUTIONS, CURVES
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We give a new method in order to obtain Weil-Serre type hounds on the minimum distance of arbitrary cyclic codes over F(pe) of length coprime to p, where e >= 1 is an arbitrary integer. In an earlier paper we obtained Weil-Serre type bounds for such codes only when e = 1 or e = 2 using lengthy explicit factorizations, which seems hopeless to generalize. The new method avoids such explicit factorizations and it produces an effective alternative. Using our method we obtain Weil-Serre type bounds in various cases. By examples we show that our bounds perform very well against Bose-Chaudhuri-Hocquenghem (BCH) bound and they yield the exact minimum distance in some cases.