Quantum codes from skew constacyclic codes over Fp m + vFp m + v2Fp m

Abstract

For an odd prime p and m ≥ 1, let $\mathcal{R} = {\mathbb{F}_{{p^m}}}[v]/\left\langle {{v^3} = v} \right\rangle $. Here our aim is to construct new non-binary quantum codes from skew constacyclic codes over this non-chain ring ℛ. In order to achieve our goal, first we study the structural properties of skew constacyclic codes and their Euclidean duals over the ring ℛ. Then we determine a necessary and sufficient condition for these codes to contain their Euclidean duals. Finally, by applying CSS construction on these dual containing skew constacyclic codes and using Gray map, we obtain several new quantum codes.