Inverse Quasi-Cyclic Codes and Automorphism Cyclic Codes

Abstract

Certain information is included to introduce cyclic codes on the finite ring. These are the
structure of the ring, its status as a linear code, weight function and distance concepts. Here the Lee
weight function is given for the ring. An automorphism is defined on the ring. With the help of defined
function, the composition of automorphism cyclic codes was constructed. A separate isometry is defined
to determine the correspondences of the codes on the rings on the objects. Then, the definition of the
inverse quasi-cyclic code is given and certain propositions and theorems are presented. It has been shown
that the image code of a code under isometry and the inverse quasi-cyclic shift transformation are the
same code as automorphism and the image of a cyclic code under isometry is the same code. Moreover,
the results and proofs regarding the written permutation, inverse quasi-cyclic code and automorphism
cyclic codes are included.