{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:11:04Z","timestamp":1761059464537},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,1,9]],"date-time":"2013-01-09T00:00:00Z","timestamp":1357689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2014,7]]},"DOI":"10.1007\/s10623-012-9790-3","type":"journal-article","created":{"date-parts":[[2013,1,8]],"date-time":"2013-01-08T23:33:21Z","timestamp":1357688001000},"page":"21-31","source":"Crossref","is-referenced-by-count":5,"title":["The Kakeya problem: a gap in the spectrum and classification of the smallest examples"],"prefix":"10.1007","volume":"72","author":[{"given":"A.","family":"Blokhuis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"De Boeck","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Mazzocca","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L.","family":"Storme","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,1,9]]},"reference":[{"key":"9790_CR1","doi-asserted-by":"crossref","unstructured":"Assmus E.F., Key J.D.: Designs and their codes. Cambridge University Press, New York (1992).","DOI":"10.1017\/CBO9781316529836"},{"key":"9790_CR2","unstructured":"Blokhuis A., Bruen A.A.: The minimal number of lines intersected by a set of $$q+2$$ points, blocking sets, and intersecting circles. J. Comb. Theory Ser. A 50, 308\u2013315 (1989)."},{"key":"9790_CR3","unstructured":"Blokhuis A., Mazzocca F.: The finite field Kakeya problem. In: Gr\u00f6tschel M., Katona G.O.H. (eds.) Building Bridges Between Mathematics and Computer Science. Bolyai Society Mathematical Studies, Vol. 19, pp. 205\u2013218 (2008)."},{"key":"9790_CR4","doi-asserted-by":"crossref","unstructured":"Dvir Z.: On the size of kakeya sets in finite fields. J. Am. Math. Soc. 22, 1093\u20131097 (2009).","DOI":"10.1090\/S0894-0347-08-00607-3"},{"key":"9790_CR5","doi-asserted-by":"crossref","unstructured":"Dvir Z., Kopparty S., Saraf S., Sudan M.: Extensions to the method of multiplicities, with applications to Kakeya sets and mergers. In: FOCS 09 (to appear) (2009).","DOI":"10.1109\/FOCS.2009.40"},{"key":"9790_CR6","unstructured":"Faber X.W.C.: On the finite field Kakeya problem in two dimensions. J. Number Theory 117, 471\u2013481 (2006)."},{"key":"9790_CR7","unstructured":"G\u00e1cs A.: Weiner Zs.: On $$(q+t)$$ -arcs of type $$(0,2, t)$$ . Des. Codes Cryptogr. 29(1\u20133), 131\u2013139 (2003)."},{"key":"9790_CR8","doi-asserted-by":"crossref","unstructured":"Hirschfeld J.W.P.: Projective geometries over finite fields. Oxford Mathematical Monographs, 2nd edn. The Clarendon Press, New York, xiv+555 pp (1998).","DOI":"10.1093\/oso\/9780198502951.001.0001"},{"key":"9790_CR9","doi-asserted-by":"crossref","unstructured":"Hirschfeld J.W.P., Korchm\u00e1ros G.: Arcs and curves over a finite field. Finite Fields Appl. 5, 393\u2013408 (1999).","DOI":"10.1006\/ffta.1999.0260"},{"key":"9790_CR10","unstructured":"Key J.D., McDonough T.P., Mavron V.C.: An upper bound for the minimum weight of the dual codes of desarguesian planes. Eur. J. Comb. 30(1), 220\u2013229 (2009)."},{"key":"9790_CR11","unstructured":"Korchm\u00e1ros G., Mazzocca F.: On $$(q+t)$$ -arcs of type $$(0,2, t)$$ in a desarguesian plane of order $$q$$ . Math. Proc. Camb. Phil. Soc. 108(3), 445\u2013459 (1990)."},{"key":"9790_CR12","unstructured":"Lavrauw M., Storme L., Van de Voorde G.: Linear codes from projective spaces. In: Bruen A.A., Wehlau D.L. (eds.) Error-Correcting Codes, Finite Geometries, and Cryptography. AMS Contemporary Mathematics (CONM) Book Series, vol. 523, pp. 185\u2013202 (2010)."},{"key":"9790_CR13","doi-asserted-by":"crossref","unstructured":"Saraf S., Sudan M.: Improved lower bound on the size of Kakeya sets over finite fields. Anal. PDE 1(3), 375\u2013379 (2008)","DOI":"10.2140\/apde.2008.1.375"},{"key":"9790_CR14","doi-asserted-by":"crossref","unstructured":"Segre B.: Ovals in finite projective planes. Can. J. Math. 7, 414\u2013416 (1955).","DOI":"10.4153\/CJM-1955-045-x"},{"key":"9790_CR15","unstructured":"Tao T.: Poincar\u00e9s legacies: pages from year two of a mathematical blog. American Mathematical Society, vol. I (2009)."},{"key":"9790_CR16","unstructured":"Wolff T.: Recent Work Connected with the Kakeya Problem. Prospects in Mathematics (Princeton, NJ, 1996). American Mathematical Society, Providence, RI, pp. 129\u2013162 (1999)."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-012-9790-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-012-9790-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-012-9790-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,4]],"date-time":"2024-05-04T13:26:35Z","timestamp":1714829195000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-012-9790-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,9]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,7]]}},"alternative-id":["9790"],"URL":"https:\/\/doi.org\/10.1007\/s10623-012-9790-3","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1,9]]}}}