Supersingular curves over finite fields and weight divisibility of codes

• Autores: Cem Güneri, Gary McGuire
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 259, Nº 2, 2014, págs. 474-484
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.12.017
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• Resumen

  • 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.