English

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 qq-ary optimal locally repairable codes with lengths that can extend to q+2qq+2\sqrt{q}. In this paper, we generalize their methods to hyperelliptic curves of genus 22, resulting in the construction of several new families of qq-ary optimal or almost optimal locally repairable codes. Our codes feature lengths that can approach q+4qq+4\sqrt{q}, and the locality can reach up to 239239.

Keywords

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}
}
R2 v1 2026-06-28T21:48:11.630Z