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) AbstractMotivated 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 |
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Uncontrolled Keywords: | Supersingular curve, cyclic code, quasi-cyclic code, trace representation |
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Subjects: | Q Science > QA Mathematics |
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ID Code: | 21350 |
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Deposited By: | Cem Güneri |
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Deposited On: | 24 Dec 2012 09:55 |
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Last Modified: | 01 Aug 2019 10:04 |
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