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.