The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic codes and almost quasi-cyclic codes are discussed in detail, presenting necessary and sufficient conditions for which linear codes with such an automorphism are self-orthogonal, self-dual, or linear complementary dual.

翻译：本文旨在阐述具有m阶置换自同构的有限域q元线性码的结构。这些码可视为广义准循环码。详细讨论准循环码与几乎准循环码，给出具有此类自同构的线性码为自正交、自对偶或线性互补对偶的充要条件。