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On cyclic algebraic-geometry codes (2106.08884v1)
Published 1 Jun 2021 in math.AG, cs.IT, math.CO, math.IT, and math.NT
Abstract: In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms. We prove that cyclic algebraic geometry codes constructed in this way are closely related to cyclic extensions. We also give a detailed study of the monomial equivalence of cyclic algebraic geometry codes constructed with our method in the case of a rational function field.