Multidimensional cyclic codes and Artin-Schreier type hypersurfaces over finite fields

Guneri C., Ozbudak F.

FINITE FIELDS AND THEIR APPLICATIONS, cilt.14, sa.1, ss.44-58, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 1
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1016/j.ffa.2006.12.003
  • Dergi Adı: FINITE FIELDS AND THEIR APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.44-58
  • Anahtar Kelimeler: multidimensional cyclic code, Artin-Schreier type hypersurface, Deligne's inequality, Hasse-Weil-Serre inequality
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We obtain a trace representation for multidimensional cyclic codes via Delsarte's theorem. This relates the weights of the codewords to the number of affine rational points of Artin-Schreier type hypersurfaces over finite fields. Using Deligne's and Hasse-Weil-Serre inequalities we get bounds on the minimum distance. Comparison of the bounds is made and illustrated by examples. Some applications of our results are given. We obtain a bound on certain character sums over F-2 which gives better estimates than Deligne's inequality in some cases. We also improve the minimum distance bounds of Moreno-Kumar on p-ary subfield subcodes of generalized Reed-Muller codes for some parameters. (c) 2006 Elsevier Inc. All rights reserved.