Stabilizer quantum codes defined by trace-depending polynomials
Information Theory
2024-10-25 v2 math.IT
Abstract
Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace. In this paper, we propose to evaluate polynomials at the roots of trace-depending polynomials (given by a constant plus the trace of a polynomial) and show that this procedure gives rise to stabilizer quantum error-correcting codes with a wider range of lengths than in other papers involving roots of the trace and with excellent parameters. Namely, we are able to provide new binary records and non-binary codes improving the ones available in the literature.
Cite
@article{arxiv.2208.06187,
title = {Stabilizer quantum codes defined by trace-depending polynomials},
author = {Carlos Galindo and Fernando Hernando and Helena Martín-Cruz and Diego Ruano},
journal= {arXiv preprint arXiv:2208.06187},
year = {2024}
}