Inverse Quasi Cyclic Code and Application in Chain Ring

Abstract

The existence of inverse quasi-cyclic codes in the 2 2 F F + u ring is presented. Here, Gray transform and inverse quasi cyclic code definitions are given first. Afterwards, its relationship with automorphism and cyclic codes is mentioned. The proposition including Nechaev permutation, quasi cyclic codes and Gray transformation is explained. From this it is concluded that inverse quasi cyclic codes correspond to Gray images of the cyclic code. Finally, a 4-length repeat code example is included regarding this topic.