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
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Cem Güneri
Date Deposited: 24 Dec 2012 09:55
Last Modified: 01 Aug 2019 10:04
URI: https://research.sabanciuniv.edu/id/eprint/21350

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