LOCALLY REPAIRABLE CODES WITH HIGH AVAILABILITY BASED ON GENERALISED QUADRANGLES

Locally Repairable Codes (LRC's) based on generalised quadran-gles 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 deter-mine the minimum weight of the codes of translation generalised quadrangles and characterise the codewords of minimum weight.