Quantum codes obtained through (1+(p−2)ν)-constacyclic codes over Zp+νZp

Abstract

This paper is concerned with, structural properties and construction of quantum codes over Z_p by using (1+(p−2)ν)-Constacyclic codes over the finite commutative non-chain ring ℜ = Z_p+νZ_p where ν² = ν and Z_p is field having p elements with characteristic p where p is prime. A Gray map is defined between ℜ and Z_p². The parameters of quantum codes over Z_p are obtained by decomposing (1+(p−2)ν)-constacyclic codes into cyclic and negacyclic codes over Z_p. As an application, some examples of quantum codes of arbitrary length, are also obtained.