The Subfield Metric and its Application to Quantum Error Correction
Information Theory
2024-06-26 v2 math.IT
Quantum Physics
Abstract
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric quantum codes. We set up the theoretic framework for this weight and metric, including upper and lower bounds, asymptotic behavior of random codes, and we show the existence of an optimal family of codes achieving the Singleton-type upper bound.
Cite
@article{arxiv.2212.00431,
title = {The Subfield Metric and its Application to Quantum Error Correction},
author = {Markus Grassl and Anna-Lena Horlemann and Violetta Weger},
journal= {arXiv preprint arXiv:2212.00431},
year = {2024}
}