A generalization of the construction of quantum codes from Hermitian self-orthogonal codes

An important strength of the $q$-ary stabilizer quantum codes is that they can be constructed from Hermitian self-orthogonal $q^2$-ary linear codes. We prove that this result can be extended to $q^{2^\ell}$-ary linear codes, $\ell > 1$, and give a result for easily obtaining codes of the last type. As a consequence we provide several new binary stabilizer quantum codes which are records according to \cite{codet} and new $2 \neq q$-ary ones improving others in the literature.