Decompositions of vector spaces over GF(2) into disjoint equidimensional affine spaces

Partitions of the 8-dimensional vector s

Partitions of the 8-dimensional vector space over GF(2)

✍ S. El-Zanati; O. Heden; G. Seelinger; P. Sissokho; L. Spence; C. Vanden Eynden 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 128 KB

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) =