Application of Constacyclic Codes over the Semi Local Ring Fp M+vfp M

Abstract

In this paper, we study the quantum codes over F<inf>p</inf> m, which are obtained from (λ<inf>1</inf> + λ<inf>2</inf>)-constacyclic codes over the semi local ring F<inf>p</inf> m + vF<inf>p</inf> m, where v2 = 1, p is odd prime. We decompose a (λ<inf>1</inf> + λ<inf>2</inf>)-constacyclic code over F<inf>p</inf> m + vF<inf>p</inf> m into two constacyclic codes over F<inf>p</inf> m such as (λ<inf>1</inf> + λ<inf>2</inf>)-constacyclic and (λ<inf>1</inf>–λ<inf>2</inf>)-constacyclic. We give the necessary and sufficient condition that the (λ<inf>1</inf> + vλ<inf>2</inf>)-constacyclic codes over F<inf>p</inf> m + vF<inf>p</inf> m contain their duals. We give some examples of non binary quantum codes. © 2020, Indian National Science Academy.