{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:31:46Z","timestamp":1787232706201,"version":"3.56.0"},"reference-count":42,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100009448","name":"Universit\u00e0 degli Studi della Campania Luigi Vanvitelli","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100009448","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Gruppo Nazionale per l\u2019Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","award":["E53C23001670001"],"award-info":[{"award-number":["E53C23001670001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Algebra Geometry"],"published-print":{"date-parts":[[2024,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Clubs of rank [Formula: see text] are well-celebrated objects in finite geometries introduced by Fancsali and Sziklai in 2006. After the connection with a special type of arc known as a KM-arc, they renewed their interest. This paper aims to study clubs of rank [Formula: see text] in [Formula: see text]. We provide a classification result for [Formula: see text]-clubs of rank [Formula: see text], and we analyze the [Formula: see text]-equivalence of the known subspaces defining clubs; for some of them the problem is then translated into determining whether or not certain scattered spaces are equivalent.\u00a0Then we find a polynomial description of the known families of clubs via some linearized polynomials.\u00a0Then we apply our results to the theory of blocking sets, KM-arcs, polynomials, and rank metric codes, obtaining new constructions and classification results.<\/jats:p>","DOI":"10.1137\/22m1523534","type":"journal-article","created":{"date-parts":[[2024,8,12]],"date-time":"2024-08-12T04:02:49Z","timestamp":1723435369000},"page":"493-518","source":"Crossref","is-referenced-by-count":2,"title":["Clubs and Their Applications"],"prefix":"10.1137","volume":"8","author":[{"given":"Vito","family":"Napolitano","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi della Campania \u201cLuigi Vanvitelli,\u201d I\u201381100 Caserta, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olga","family":"Polverino","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi della Campania \u201cLuigi Vanvitelli,\u201d I\u201381100 Caserta, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paolo","family":"Santonastaso","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi della Campania \u201cLuigi Vanvitelli,\u201d I\u201381100 Caserta, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5087-2363","authenticated-orcid":true,"given":"Ferdinando","family":"Zullo","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi della Campania \u201cLuigi Vanvitelli,\u201d I\u201381100 Caserta, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,8,12]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004117000044"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-016-3529-0"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2003.09.006"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1998.2915"},{"key":"ref5","volume":"109","author":"Bartoli D.","year":"2022","journal-title":"J. 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