Construction of asymptotically good locally repairable codes via automorphism groups of function fields

TL;DR

This paper introduces a new construction method for asymptotically good locally repairable codes using automorphism groups of function fields, enhancing flexibility and improving bounds for large alphabets.

Contribution

It extends existing constructions via automorphism groups, allowing more flexible locality and providing improved bounds on locally repairable codes.

Findings

Construction allows more flexible locality.

Improved Gilbert-Varshamov bound for large q.

Extends previous work using automorphism groups.

Abstract

Locally repairable codes have been investigated extensively in recent years due to practical application in distributed storage as well as theoretical interest. However, not much work on asymptotical behavior of locally repairable codes has been done until now. In particular, there is a little result on constructive lower bound on asymptotical behavior of locally repairable codes. In this paper, we extend the construction given in \cite{BTV17} via automorphism groups of function field towers. The main advantage of our construction is to allow more flexibility of locality. Furthermore, we show that the Gilbert-Varshamov type bound on locally repairable codes can be improved for all sufficiently large alphabet size $q$.