✦ LIBER ✦
Partitions of the 8-dimensional vector space over GF(2)
✍ Scribed by S. El-Zanati; O. Heden; G. Seelinger; P. Sissokho; L. Spence; C. Vanden Eynden
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 128 KB
- Volume
- 18
- Category
- Article
- ISSN
- 1063-8539
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✦ Synopsis
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 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).