On the generalization of the construction of 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 $q^{2m}$-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 $q\ne 2$, improving others in the literature.

References in corpus (1)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"

Cited by in corpus (3)

• Quantum $(r,\delta )$-locally recoverable codes
• Stabilizer quantum codes defined by trace-depending polynomials
• Steane enlargement of Entanglement-Assisted Quantum Error-Correcting Codes