Güneri, Cem and McGuire, Gary (2014) Supersingular curves over finite fields and weight divisibility of codes. Journal of Computational and Applied Mathematics, 259 (Part: ). 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 |
| Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |
| Depositing User: | Cem Güneri |
| Date Deposited: | 23 Feb 2014 22:09 |
| Last Modified: | 26 Apr 2022 09:12 |
| URI: | https://research.sabanciuniv.edu/id/eprint/24023 |
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Supersingular curves over finite fields and weight divisibility of codes. (deposited 24 Dec 2012 09:55)
- Supersingular curves over finite fields and weight divisibility of codes. (deposited 23 Feb 2014 22:09) [Currently Displayed]
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