ArtinSchreier curves and weights of two dimensional cyclic codes
Güneri, Cem (2003) ArtinSchreier curves and weights of two dimensional cyclic codes. (Accepted/In Press) AbstractLet GF(q) be the finite field with q elements of characteristic p, GF(q^m) be the extension of degree m>1 and f(x) be a polynomial over GF(q^m). We determine a necessary and sufficient condition for y^qy=f(x) to have the maximum number of affine GF(qm)rational points. Then we study the weights of 2D cyclic codes. For this, we give a trace representation of the codes starting with the zeros of the dual 2D cyclic code. This leads to a relation between the weights of codewords and a family of ArtinSchreier curves.We give a lower bound on the minimum distance for a large class of 2D cyclic codes. Then we look at some special classes that are not covered by our main result and obtain similar minimum distance bounds. Item Type:  Article 

Uncontrolled Keywords:  ArtinSchreier curve, 2D cyclic code, trace code. 

Subjects:  Q Science > QA Mathematics 

ID Code:  349 

Deposited By:  Cem Güneri 

Deposited On:  08 Dec 2006 02:00 

Last Modified:  26 Oct 2007 16:26 

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