Multidimensional cyclic codes and Artin-Schreier type hypersurfaces over finite fields
FINITE FIELDS AND THEIR APPLICATIONS, cilt.14, sa.1, ss.44-58, 2008 (SCI-Expanded, Scopus)
- 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.