LRC codes over characteristic $2$

Francisco Galluccio

LRC codes over characteristic $2$

Information Theory 2026-04-07 v1 math.IT Number Theory

Authors: Francisco Galluccio

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.

Keywords

locally repairable codes coding theory maximum distance separable code

Cite

@article{arxiv.2604.04678,
  title  = {LRC codes over characteristic $2$},
  author = {Francisco Galluccio},
  journal= {arXiv preprint arXiv:2604.04678},
  year   = {2026}
}

Comments

18 pages, 6 figures, 1 table, 1 image

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