On Optimal Locally Repairable Codes with Super-Linear Length

TL;DR

This paper derives new upper bounds on the length of optimal locally repairable codes, constructs codes that meet these bounds with super-linear length, and generalizes previous bounds for improved understanding.

Contribution

It introduces new upper bounds on the length of optimal locally repairable codes and constructs codes that achieve these bounds with super-linear length.

Findings

New upper bounds on code length are established.

Constructed codes are super-linear in alphabet size.

Bounds generalize and improve previous results.

Abstract

Locally repairable codes which are optimal with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve and generalize previously known bounds. Optimal codes are constructed, whose length is order-optimal when compared with the new upper bounds. The length of the codes is super-linear in the alphabet size.