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)
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.
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