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) AbstractWe 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 ArtinSchreier hypersurfaces defined over certain finite fields. Using Deligne’s and Hasse WeilSerre 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 MorenoKumar on pary subfield subcodes of generalized ReedMuller codes for some parameters. We also characterize qm optimal and maximal ArtinSchreier hypersurfaces. Item Type:  Article 

Uncontrolled Keywords:  multidimensional cyclic code; ArtinSchreier hypersurface; Deligne’s inequality; HasseWeilSerre 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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