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Locally repairable codes with high availability based on generalised quadrangles

Michel Lavrauw, ,Faculty of Engineering and Natural Sciences, Sabancı University, 34956 Orhanlı, Tuzla, Istanbul, Turkey, Geertrui Van de Voorde, ,School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, 8140 Christchurch, New Zealand
<span title="">2019</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jbbcig2iqnbuvngg7spzuoozwu" style="color: black;">Advances in Mathematics of Communications</a> </i> &nbsp;

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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
more &raquo; ... ht. 2020 Mathematics Subject Classification: 51E12,51E20,94B05.
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Citation

Michel Lavrauw, ,Faculty of Engineering and Natural Sciences, Sabancı University, 34956 Orhanlı, Tuzla, Istanbul, Turkey, Geertrui Van de Voorde, ,School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, 8140 Christchurch, New Zealand. "Locally repairable codes with high availability based on generalised quadrangles." Advances in Mathematics of Communications 0.0 (2019) 0-0