AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves

Abstract

We investigate several types of linear codes constructed from two families ${\tilde{\mathcal{S}}}_q$ and ${\tilde{\mathcal{R}}}_q$ of maximal curves over finite fields recently constructed by Skabelund as cyclic covers of the Suzuki and Ree curves. Plane models for such curves are provided, and the Weierstrass semigroup $H(P)$ at an ${\mathbb{F}}_q$-rational point $P$ is shown to be symmetric.

arXiv admin note: text overlap with arXiv:1703.03178