LRC codes over characteristic $2$

TL;DR

This paper completes the construction of LRC codes over characteristic 2, providing a general method for large-length codes with specific parameters and analyzing special cases for q=4 and q=8.

Contribution

It introduces a comprehensive construction for linear LRC codes over characteristic 2, enabling large code lengths and specific locality parameters.

Findings

Constructed LRC codes with length approximately q^4

Achieved codes with dimension and distance of order q^4

Analyzed special cases for q=4 and q=8

Abstract

In this work the construction of LRC codes given in [6] is completed, in the case of even characteristic. A general construction is presented, that enables us to obtain linear LRC codes of large length $n \approx q^4$, dimension and distance of order $q^4$, and locality $r =q-1$. In addition, the cases $q = 4$ and $q=8$ are studied.