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Codes Cryptogr."],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A perfect matroid design (PMD) is a matroid whose flats of the same rank all have the same size. In this paper we introduce the <jats:italic>q<\/jats:italic>-analogue of a PMD and its properties. In order to do so, we first establish a new cryptomorphic definition for <jats:italic>q<\/jats:italic>-matroids. We show that <jats:italic>q<\/jats:italic>-Steiner systems are examples of <jats:italic>q<\/jats:italic>-PMD\u2019s and we use this <jats:italic>q<\/jats:italic>-matroid structure to construct subspace designs from <jats:italic>q<\/jats:italic>-Steiner systems. We apply this construction to the only known <jats:italic>q<\/jats:italic>-Steiner system, which has parameters <jats:italic>S<\/jats:italic>(2,\u00a03,\u00a013;\u00a02), and hence establish the existence of a new subspace design with parameters 2-(13,\u00a04,\u00a05115;\u00a02).<\/jats:p>","DOI":"10.1007\/s10623-022-01087-3","type":"journal-article","created":{"date-parts":[[2022,10,2]],"date-time":"2022-10-02T14:02:26Z","timestamp":1664719346000},"page":"451-473","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Constructions of new matroids and designs over $${\\mathbb {F}}_q$$"],"prefix":"10.1007","volume":"91","author":[{"given":"Eimear","family":"Byrne","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michela","family":"Ceria","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sorina","family":"Ionica","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9906-9109","authenticated-orcid":false,"given":"Relinde","family":"Jurrius","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elif","family":"Sa\u00e7\u0131kara","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,10,2]]},"reference":[{"key":"1087_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-6666-3","volume-title":"Combinatorial Theory","author":"M Aigner","year":"1979","unstructured":"Aigner M.: Combinatorial Theory. 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