New non-binary quantum codes from skew constacyclic codes over the ring ${\mathbb{F}}_{p^m}+v{\mathbb{F}}_{p^m}+v^2{\mathbb{F}}_{p^m}$

Abstract

In this article, we construct new non-binary quantum codes from skew constacyclic codes over finite commutative non-chain ring $\mathcal{R}={\mathbb{F}}_{p^m}[v]/⟨v^3=v⟩$ where $p$ is an odd prime and $m\ge 1$. In order to obtain such quantum codes, first we study the structural properties of skew constacyclic codes and their Euclidean duals over the ring $\mathcal{R}$. Then a necessary and sufficient condition for skew constacyclic codes over $\mathcal{R}$ to contain their Euclidean duals is established. Finally, with the help of CSS construction and using Gray map, many new non-binary quantum codes are obtained over ${\mathbb{F}}_{p^m}$.

Accepted in ACCT-2020 conference for proceeding