Quantum Codes Obtained through Constacyclic Codes over Z3 + νZ3 + ωZ3 + νωZ3

Abstract

This paper is concerned with, structural properties and construction of quantum codes over Z3 by using constacyclic codes over the finite commutative non-chain ring R = Z3 + νZ3 + ωZ3 + νωZ3 where ν2 = 1, ω2 = ω, νω = νω, and Z3 is field having 3 elements with characteristic 3. A Gray map is defined between R and Z43. The parameters of quantum codes over Z3 are obtained by decomposing constacyclic codes into cyclic and negacyclic codes over Z3. As an application, some examples of quantum codes of arbitrary length, are also obtained.