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Partitions of the 8-Dimensional Vector Space Over GF(2)
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
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2010 (English)In: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 18, no 6, 462-474 p.Article in journal (Refereed) Published
Abstract [en]

Let V=V(n,q) denote the vector space of dimension n over GF(q). A set of subspaces of V is called a partition of V if every nonzero vector in V is contained in exactly one subspace of V. Given a. partition P of V with exactly a(i) subspaces of dimension i for 1 <= i <= n, we have Sigma(n)(i=1) a(i)(q(i)-1) = q(n)-1, and we call the n-tuple (a(n), a(n-1), ..., a(1)) the type of P. In this article we identify all 8-tuples (a(8), a(7), ..., a(2), 0) that are the types of partitions of V(8,2).

Place, publisher, year, edition, pages
2010. Vol. 18, no 6, 462-474 p.
Keyword [en]
Vector space partition
National Category
URN: urn:nbn:se:kth:diva-27074DOI: 10.1002/jcd.20247ISI: 000283762200004OAI: diva2:376358
QC 20101210Available from: 2010-12-10 Created: 2010-12-06 Last updated: 2010-12-10Bibliographically approved

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Heden, Olof
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Mathematics (Div.)
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