Codes with hierarchical locality on Artin–Schreier surfaces

In this paper, we construct codes with hierarchical locality using natural geometric structures in Artin–Schreier surfaces of the form [Formula: see text]. Our main theorem describes the codes, their hierarchical structure and recovery algorithms, and gives parameters. We also develop a family of examples using codes defined over [Formula: see text] on the surface [Formula: see text]. We use elementary methods to count the [Formula: see text]-rational points on the surface, enabling us to provide explicit hierarchical parameters and a better bound on minimum distance for these codes. An additional example and some generalizations are also considered.