{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T09:36:42Z","timestamp":1648546602251},"reference-count":15,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AMC"],"published-print":{"date-parts":[[2022]]},"abstract":"<p style='text-indent:20px;'>Locally Repairable Codes (LRC's) based on generalised quadrangles were introduced by Pamies-Juarez, Hollmann and Oggier in [<xref ref-type=\"bibr\" rid=\"b3\">3<\/xref>], 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.<\/p><\/jats:p>","DOI":"10.3934\/amc.2020099","type":"journal-article","created":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T11:15:12Z","timestamp":1596453312000},"page":"73","source":"Crossref","is-referenced-by-count":0,"title":["Locally repairable codes with high availability based on generalised quadrangles"],"prefix":"10.3934","volume":"16","author":[{"given":"Michel","family":"Lavrauw","sequence":"first","affiliation":[]},{"given":"Geertrui","family":"Van de Voorde","sequence":"additional","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/amc.2020099-1","doi-asserted-by":"publisher","unstructured":"E. F. Assmus, Jr., J. D. Key., Designs and Their Codes<\/i>, ${ref.volume}<\/b> (1992).","DOI":"10.1017\/CBO9781316529836"},{"key":"key-10.3934\/amc.2020099-2","doi-asserted-by":"publisher","unstructured":"B. Bagchi, N. S. N. Sastry.Codes associated with generalized polygons, Geom. Dedicata<\/i>, 27<\/b> (1988), 1-8.","DOI":"10.1007\/BF00181609"},{"key":"key-10.3934\/amc.2020099-3","doi-asserted-by":"publisher","unstructured":"L. Pamies-Juarez, H. D. L. Hollmann and F. Oggier, Locally repairable codes with multiple repair alternatives, In IEEE International Symposium on Information Theory - Proceedings (ISIT)<\/i>, 2013,892\u2013896.","DOI":"10.1109\/ISIT.2013.6620355"},{"key":"key-10.3934\/amc.2020099-4","doi-asserted-by":"publisher","unstructured":"P. Delsarte, J. M. Goethals, F. J. MacWilliams.On generalized Reed-Muller codes and their relatives, Information and Control<\/i>, 16<\/b> (1970), 403-442.","DOI":"10.1016\/S0019-9958(70)90214-7"},{"key":"key-10.3934\/amc.2020099-5","doi-asserted-by":"publisher","unstructured":"P. Gopalan, C. Huang, H. Simitci, and S. Yekhanin.On the locality of codeword symbols, IEEE Trans. Inform. 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Lavrauw, Scattered Subspaces with Respect to Spreads and Eggs in Finite Projective Spaces<\/i>, PhD thesis, Technical University of Eindhoven, The Netherlands, 2001."},{"key":"key-10.3934\/amc.2020099-10","doi-asserted-by":"publisher","unstructured":"M. Lavrauw and G. Van de Voorde, Field reduction and linear sets in finite geometry, Topics in Finite Fields<\/i>, Contemp. Math., volume 632, Amer. Math. Soc., Providence, RI, 2015,271\u2013293.","DOI":"10.1090\/conm\/632\/12633"},{"key":"key-10.3934\/amc.2020099-11","unstructured":"S. E. Payne and J. A. Thas, Finite Generalized Quadrangles<\/i>, Pitman Advanced Publishing Program, Boston, MA, 1984."},{"key":"key-10.3934\/amc.2020099-12","doi-asserted-by":"publisher","unstructured":"V. Pepe, L. Storme, G. Van de Voorde.Small weight codewords in the LDPC codes arising from linear representations of geometries, J. Combin. 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