Supersingular curves over finite fields and weight divisibility of codes

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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


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:02 Aug 2019 09:58

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