Optimal and Almost Optimal Locally Repairable Codes from Hyperelliptic Curves
Information Theory
2025-02-19 v1 math.IT
Abstract
Locally repairable codes are widely applicable in contemporary large-scale distributed cloud storage systems and various other areas. By making use of some algebraic structures of elliptic curves, Li et al. developed a series of -ary optimal locally repairable codes with lengths that can extend to . In this paper, we generalize their methods to hyperelliptic curves of genus , resulting in the construction of several new families of -ary optimal or almost optimal locally repairable codes. Our codes feature lengths that can approach , and the locality can reach up to .
Cite
@article{arxiv.2502.12493,
title = {Optimal and Almost Optimal Locally Repairable Codes from Hyperelliptic Curves},
author = {Junjie Huang and Chang-An Zhao},
journal= {arXiv preprint arXiv:2502.12493},
year = {2025}
}