# American Institute of Mathematical Sciences

February  2022, 16(1): 73-81. doi: 10.3934/amc.2020099

## Locally repairable codes with high availability based on generalised quadrangles

 1 Faculty of Engineering and Natural Sciences, Sabancı University, 34956 Orhanlı, Tuzla, Istanbul, Turkey 2 School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, 8140 Christchurch, New Zealand

* Corresponding author: Geertrui Van de Voorde

Received  February 2020 Revised  May 2020 Published  February 2022 Early access  July 2020

Locally Repairable Codes (LRC's) based on generalised quadrangles were introduced by Pamies-Juarez, Hollmann and Oggier in [3], 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.

Citation: Michel Lavrauw, Geertrui Van de Voorde. Locally repairable codes with high availability based on generalised quadrangles. Advances in Mathematics of Communications, 2022, 16 (1) : 73-81. doi: 10.3934/amc.2020099
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