An alternative proof of a result on the weight divisibility of a cyclic code using supersingular curves

Abstract

We present an alternative proof of a result of Zeng–Shan–Hu that shows that the cyclic code with three zeros α, α3, α13 has the same weight distribution as the 3-error-correcting BCH code. Our proof uses the theory of algebraic curves over finite fields, and combines results that are already in the literature. This method is applicable in other cases too.