Supersingular curves over finite fields and weight divisibility of codes

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. (C) 2013 Elsevier B.V. All rights reserved.