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

Date

2008-1

Author

Güneri, Cem
Özbudak, Ferruh

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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.

Subject Keywords

Multidimensional cyclic code, Artin-Schreier type hypersurface, Deligne's inequality, Hasse-Weil-Serre inequality

URI

https://hdl.handle.net/11511/28265

Journal

Finite Fields and Their Applications

DOI

https://doi.org/10.1016/j.ffa.2006.12.003

Collections

Department of Mathematics, Article

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Citation Formats

C. Güneri and F. Özbudak, “Multidimensional cyclic codes and Artin–Schreier type hypersurfaces over finite fields,” Finite Fields and Their Applications, pp. 44–58, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/28265.