Improving the dimension bound of Hermitian Lifted Codes

TL;DR

This paper enhances the theoretical bounds on the dimension and rate of Hermitian Lifted Codes, achieving a higher asymptotic rate through elementary polynomial division techniques, especially for fields where q is a power of 2.

Contribution

It introduces a new method using univariate polynomial division to improve the dimension bounds of Hermitian Lifted Codes, surpassing previous estimates.

Findings

Improved asymptotic rate estimate to 0.010 for q a power of 2

Enhanced dimension bounds for Hermitian Lifted Codes

Utilized elementary polynomial division for code analysis

Abstract

In this article we improve the dimension and minimum distance bound of the the Hermitian Lifted Codes LRCs construction from L\'opez, Malmskog, Matthews, Pi\~nero and Wooters (L\'opez et. al.) via elementary univariarte polynomial division. They gave an asymptotic rate estimate of $0.007$. For the case where $q$ is a power of $2$ we improve the rate estimate to $0.010$ using univariate polynomial division.