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.

翻译：在本文中,我们开始研究周期代数几何码,我们用其一组自制形态来提供条件,在定界的代数函数场范围内,利用这些代数函数场来构建循环代数几何码,我们证明以这种方式构建的循环代数几何码与周期扩展密切相关,我们还详细研究了在合理功能区的情况下,以我们的方法构建的循环代数几何码的单等性。