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

TL;DR

This paper extends the construction of quantum codes from Hermitian self-orthogonal codes to higher powers of q, providing new binary and q-ary quantum codes with record parameters.

Contribution

It generalizes the method for constructing quantum codes from Hermitian self-orthogonal codes to broader classes, yielding new codes with improved parameters.

Findings

Several new binary stabilizer quantum codes with record parameters

New q-ary quantum codes that outperform existing ones

A generalized construction method for quantum codes from Hermitian self-orthogonal codes

Abstract

Many $q$-ary stabilizer quantum codes can be constructed from Hermitian self-orthogonal $q^2$-ary linear codes. This result can be generalized to $q^{2 m}$-ary linear codes, $m > 1$. We give a result for easily obtaining quantum codes from that generalization. As a consequence we provide several new binary stabilizer quantum codes which are records according to \cite{codet} and new $q$-ary ones, with $q \neq 2$, improving others in the literature.