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Multidimensional cyclic codes and Artin–Schreier hypersurfaces over finite fields

Güneri, Cem and Özbudak, Ferruh (2006) Multidimensional cyclic codes and Artin–Schreier hypersurfaces over finite fields. (Accepted/In Press)

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Abstract

We obtain a trace representation for multidimensional cyclic codes via Delsarte’s theorem. This relates the weights of the codewords to the number of a±ne rational points of Artin-Schreier hypersurfaces defined over certain finite fields. Using Deligne’s and Hasse- Weil-Serre inequalities we state bounds on the minimum distance. Comparison of the bounds is made and illustrated by examples. Some applications of our results are given. Over F2, we obtain a bound on certain character sums giving better estimates than Deligne’s inequality in some cases. We improve the minimum distance bounds of Moreno-Kumar on p-ary subfield subcodes of generalized Reed-Muller codes for some parameters. We also characterize qm- optimal and maximal Artin-Schreier hypersurfaces.

Item Type:Article
Uncontrolled Keywords:multidimensional cyclic code; Artin-Schreier hypersurface; Deligne’s inequality; Hasse-Weil-Serre inequality.
Subjects:Q Science > QA Mathematics
ID Code:5898
Deposited By:Cem Güneri
Deposited On:26 Oct 2007 14:21
Last Modified:27 Oct 2007 13:58

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