Locally repairable codes with high availability based on generalised quadrangles

TL;DR

This paper analyzes locally repairable codes derived from generalised quadrangles, determining their repairability and availability, and characterizing minimum weight codewords to improve understanding of their repair properties.

Contribution

It provides explicit values for repairability and availability of LRCs based on generalised quadrangles and characterizes minimum weight codewords for these codes.

Findings

Calculated repairability and availability for many known generalised quadrangles.

Characterized the codewords of minimum weight in these codes.

Enhanced understanding of the repair properties of LRCs based on geometric structures.

Abstract

Locally Repairable Codes (LRC's) based on generalised quadrangles were introduced by Pamies-Juarez, Hollmann and Oggier in \cite{PaHoOg2013}, and bounds on the repairability and availability were derived. In this paper, we determine the values of the repairability and availability of such LRC's for a large portion of the currently known generalised quadrangles. In order to do so, we determine the minimum weight of the codes of translation generalised quadrangles and characterise the codewords of minimum weight.