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

2008-1
Güneri, Cem
Özbudak, Ferruh
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.
Finite Fields and Their Applications

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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.