The images of constacyclic codes and new quantum codes

Abstract

Let q be a prime power and $$m\ge 2$$ be a positive integer. A sufficient condition for the $$q^2$$-ary images of constacyclic codes over $${\mathbb {F}}_{q^{2m}}$$ to be Hermitian self-orthogonal is presented. Hermitian self-orthogonal codes over $${\mathbb {F}}_{q^{2}}$$ are obtained as the images of constacyclic codes over $${\mathbb {F}}_{q^{2m}}$$. Two classes of quantum codes are derived by employing the Hermitian construction. The construction produces quantum codes with better parameters than the previously known ones.