期刊论文

Fan, Yun(yfan@mail.ccnu.edu.cn)

英文

Finite Fields and Their Applications

1071-5797

2023

85

102127

10.1016/j.ffa.2022.102127

The research of the first author is supported by NSFC with grant number 12171289 . The authors would like to thank the editor and the anonymous reviewers for their valuable comments which helped us to improve the paper greatly.

本校为第一机构

We characterize the structure of 2-quasi-cyclic codes over a finite field F by the so-called Goursat Lemma. With the characterization, we exhibit a necessary and sufficient condition for a 2-quasi-cyclic code being a dihedral code. And we obtain a necessary and sufficient condition for a self-dual 2-quasi-cyclic code being a dihedral code (if charF=2), or a consta-dihedral code (if charF≠2). As a consequence, any self-dual 2-quasi-cyclic code generated by one element must be (consta-)dihedral. In particular, any self-dual double circulant code...