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Codes Cryptogr."],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this article, constant dimension subspace codes whose codewords have subspace distance in a prescribed set of integers, are considered. The easiest example of such an object is a <jats:italic>junta<\/jats:italic> (Combin Probab Comput 18(1\u20132):107\u2013122, 2009); i.e. a subspace code in which all codewords go through a common subspace. We focus on the case when only two intersection values for the codewords, are assigned. In such a case we determine an upper bound for the dimension of the vector space spanned by the elements of a non-junta code. In addition, if the two intersection values are consecutive, we prove that such a bound is tight, and classify the examples attaining the largest possible dimension as one of four infinite families.<\/jats:p>","DOI":"10.1007\/s10623-021-00931-2","type":"journal-article","created":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T16:47:06Z","timestamp":1634662026000},"page":"2081-2099","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On sets of subspaces with two intersection dimensions and a geometrical junta bound"],"prefix":"10.1007","volume":"90","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9323-2043","authenticated-orcid":false,"given":"Giovanni","family":"Longobardi","sequence":"first","affiliation":[]},{"given":"Leo","family":"Storme","sequence":"additional","affiliation":[]},{"given":"Rocco","family":"Trombetti","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,19]]},"reference":[{"key":"931_CR1","doi-asserted-by":"publisher","first-page":"757","DOI":"10.3934\/amc.2017055","volume":"11","author":"RD Barrolleta","year":"2017","unstructured":"Barrolleta R.D., Su\u00e1rez-Canedo E., Storme L., Vandendriessche P.: On primitive constant dimension codes and a geometrical sunflower bound. 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