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Supersingular curves over finite fields and weight divisibility of codes

Güneri, Cem and McGuire, Gary (2012) Supersingular curves over finite fields and weight divisibility of codes. (Accepted/In Press)

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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:21350
Deposited By:Cem Güneri
Deposited On:24 Dec 2012 09:55
Last Modified:23 Feb 2014 22:09

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