{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:51Z","timestamp":1753893831270,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The Galois number $G_n(q)$ is defined to be the number of subspaces of the $n$-dimensional vector space over the finite field $GF(q)$.  When $q$ is prime, we prove that $G_n(q)$ is equal to the number $L_n(q)$ of $n$-dimensional mod $q$ lattices, which are defined to be lattices (that is, discrete additive subgroups of n-space) contained in the integer lattice ${\\bf Z}^n$ and having the property that given any point $P$ in the lattice, all points of ${\\bf Z}^n$ which are congruent to $P$ mod $q$ are also in the lattice. For each $n$, we prove that $L_n(q)$ is a multiplicative function of $q$.<\/jats:p>","DOI":"10.37236\/1355","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:57:56Z","timestamp":1578707876000},"source":"Crossref","is-referenced-by-count":0,"title":["Finite Vector Spaces and Certain Lattices"],"prefix":"10.37236","volume":"5","author":[{"given":"Thomas W.","family":"Cusick","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[1998,3,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v5i1r17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v5i1r17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:09:56Z","timestamp":1579327796000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v5i1r17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,3,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1998,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1355","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1998,3,18]]},"article-number":"R17"}}