| 1. |
- El-Zanati, S., et al.
(author)
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Partitions of the 8-Dimensional Vector Space Over GF(2)
- 2010
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In: Journal of combinatorial designs (Print). - : Wiley. - 1063-8539 .- 1520-6610. ; 18:6, s. 462-474
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Journal article (peer-reviewed)abstract
- 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).
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| 2. |
- Heden, Olof, et al.
(author)
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On the type(s) of minimum size subspace partitions
- 2014
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In: Discrete Mathematics. - : Elsevier BV. - 0012-365X .- 1872-681X. ; 332, s. 1-9
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Journal article (peer-reviewed)abstract
- Let V = V(kt + r, q) be a vector space of dimension kt + r over the finite field with q elements. Let sigma(q)(kt + r, t) denote the minimum size of a subspace partition P of V in which t is the largest dimension of a subspace. We denote by n(di) the number of subspaces of dimension d(i) that occur in P and we say [d(1)(nd1),..., d(m)(ndm)] is the type of P. In this paper, we show that a partition of minimum size has a unique partition type if t + r is an even integer. We also consider the case when t + r is an odd integer, but only give partial results since this case is indeed more intricate.
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| 3. |
- Heden, Olof, et al.
(author)
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The supertail of a subspace partition
- 2013
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In: Designs, Codes and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 69:3, s. 305-316
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Journal article (peer-reviewed)abstract
- Let V = V(n, q) be a vector space of dimension n over the finite field with q elements, and let d (1) < d (2) < ... < d (m) be the dimensions that occur in a subspace partition of V. Let sigma (q) (n, t) denote the minimum size of a subspace partition of V, in which t is the largest dimension of a subspace. For any integer s, with 1 < s a parts per thousand currency sign m, the set of subspaces in of dimension less than d (s) is called the s-supertail of . The main result is that the number of spaces in an s-supertail is at least sigma (q) (d (s) , d (s-1)).
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