Güneri, Cem (2004) ArtinSchreier curves and weights of two dimensional cyclic codes. Finite Fields and Their Applications, 10 (4). pp. 481505. ISSN 10715797
This is the latest version of this item.
PDF
3011800000015.pdf
Restricted to Registered users only
Download (274kB)  Request a copy
3011800000015.pdf
Restricted to Registered users only
Download (274kB)  Request a copy
Official URL: http://dx.doi.org/10.1016/j.ffa.2003.10.002
Abstract
Let 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 
Divisions:  Faculty of Engineering and Natural Sciences 
Depositing User:  Cem Güneri 
Date Deposited:  26 Oct 2007 16:25 
Last Modified:  25 May 2011 14:11 
URI:  https://research.sabanciuniv.edu/id/eprint/5895 
Available Versions of this Item

ArtinSchreier curves and weights of two dimensional cyclic codes. (deposited 08 Dec 2006 02:00)
 ArtinSchreier curves and weights of two dimensional cyclic codes. (deposited 26 Oct 2007 16:25) [Currently Displayed]