Improvement on Parameters of Algebraic-Geometry Codes from Hermitian Curves

TL;DR

This paper improves the asymptotic parameters of algebraic-geometry codes derived from Hermitian curves, demonstrating that for large q, codes can achieve a combined dimension and minimum distance close to the code length.

Contribution

It introduces a new method showing that Hermitian codes can have a sum of dimension and minimum distance approaching the code length, improving previous bounds.

Findings

Existence of Hermitian codes with k+d >= n-3 for large q

Improved asymptotic bounds for algebraic-geometry codes from Hermitian curves

Enhanced parameters for code efficiency and error correction

Abstract

Motivated by Xing's method [7], we show that there exist [n,k,d] linear Hermitian codes over F_{q^2} with k+d>=n-3 for all sufficiently large q. This improves the asymptotic bound of Algebraic-Geometry codes from Hermitian curves given in [9,10].