New quantum codes derived from the images of constacyclic codes

Abstract

Assume that $q$ is a prime power and $m\geq 2$ is a positive integer. Cyclic codes over $\mathbb{F}_{q^{2m}}$ of length $n=\frac{q^{2m}-1}{\rho }$ with $\rho\mid (q-1)$, and constacyclic codes over $\mathbb{F}_{q^{2m}}$ of length $n=\frac{q^{2m}-1}{\rho }$ with $\rho\mid (q+1)$ are considered in this paper, respectively. Two classes of quantum codes are derived from the images of these codes by the Hermitian construction. Compared with the previously known quantum codes, the quantum codes in our scheme have better parameters.