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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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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.