Goppa code and quantum stabilizer codes from plane curves given by separated polynomials

TL;DR

This paper explores algebraic geometric codes derived from plane curves defined by separated polynomials, and constructs quantum stabilizer codes with improved parameters for reliable quantum communication.

Contribution

It introduces new algebraic geometric and quantum stabilizer codes from specific plane curves, enhancing code parameters and performance.

Findings

Quantum codes from Hermitian self-orthogonal AG codes have improved parameters.

Construction of Goppa codes from curves generated by separated polynomials.

Enhanced reliability of quantum communication networks.

Abstract

In this paper, we examine algebraic geometric (AG) codes associated with curves generated by separated polynomials, and we create AG codes and quantum stabilizer codes from these curves by varying their parameters. Our research involves a thorough examination of the curves' algebraic features as well as the creation of Goppa codes over them. Extending these findings, we create quantum stabilizer codes, revealing that quantum codes built from Hermitian self-orthogonal AG codes have acceptable parameters, improving the reliability and performance of communication networks.