QUANTUM CODES OBTAINED THROUGH $(1-2 v \omega)$-CONSTACYCLIC CODES OVER $Z_m+v Z_m+\omega Z_m+v \omega Z_m$

Abstract

In the present work, we discuss the quantum codes over the ring $Z_m, m$ is power of some odd prime. Quantum codes are obtained through $(1-2 v \omega)$-constacyclic codes over a finite non-chain ring $Z_m+v Z_m+\omega Z_m+v \omega Z_m$  with  $v^2=v, \quad \omega^2=\omega$ and $v^2 \omega^2=v \omega . \quad(1-2 v \omega)$-constacyclic codes over the ring $Z_m+v Z_m+\omega Z_m+v \omega Z_m$ are decomposed into two codes over the ring $Z_m$ in order to obtain the parameters for the corresponding quantum codes over the ring $Z_m$. Some examples of quantum codes are also provided to verify the results.

Received: September 6, 2022;
Revised: October 29, 2022;
Accepted: February 1, 2023;