Stabilizer quantum codes defined by trace-depending polynomials

TL;DR

This paper introduces a novel method for constructing stabilizer quantum error-correcting codes by evaluating polynomials at roots of trace-depending polynomials, resulting in codes with improved parameters and a wider range of lengths.

Contribution

It proposes evaluating polynomials at roots of trace-depending polynomials, expanding the range and quality of stabilizer quantum codes beyond existing methods.

Findings

Achieved new binary records for quantum codes.

Developed non-binary codes with better parameters.

Extended the range of code lengths compared to previous approaches.

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.