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Supersingular curves over finite fields and weight divisibility of codes

Güneri, Cem and McGuire, Gary (2014) Supersingular curves over finite fields and weight divisibility of codes. Journal of Computational and Applied Mathematics, 259 (Part: B). pp. 474-484. ISSN 0377-0427 (Print) 1879-1778 (Online)

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Official URL: http://dx.doi.org/10.1016/j.cam.2012.12.017

Abstract

Motivated by a recent article of the second author, we relate a family of Artin-Schreier type curves to a sequence of codes. We describe the algebraic structure of these codes, and we show that they are quasi-cyclic codes. We show that if the family of Artin-Schreier type curves consists of supersingular curves then the weights in the related codes are divisible by a certain power of the characteristic. We give some applications of the divisibility result, including showing that some weights in certain cyclic codes are eliminated in subcodes.

Item Type:Article
Uncontrolled Keywords:Supersingular curve, cyclic code, quasi-cyclic code, trace representation
Subjects:Q Science > QA Mathematics
ID Code:24023
Deposited By:Cem Güneri
Deposited On:23 Feb 2014 22:09
Last Modified:23 Feb 2014 22:09

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