A Construction of Quantum Codes via A Class of Classical Polynomial Codes

TL;DR

This paper introduces a new method for constructing classical and quantum codes using polynomial valuations, resulting in codes with improved parameters and the creation of new quantum codes.

Contribution

It presents a novel polynomial-based construction method for classical codes that also enables the generation of quantum codes with good parameters.

Findings

Classical codes with good parameters are constructed.

New quantum codes with improved parameters are developed.

The method demonstrates the potential for better quantum code constructions.

Abstract

There have been various constructions of classical codes from polynomial valuations in literature \cite{ARC04, LNX01,LX04,XF04,XL00}. In this paper, we present a construction of classical codes based on polynomial construction again. One of the features of this construction is that not only the classical codes arisen from the construction have good parameters, but also quantum codes with reasonably good parameters can be produced from these classical codes. In particular, some new quantum codes are constructed (see Examples \ref{5.5} and \ref{5.6}).