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

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 , and we call the n‐tuple (a_n, a_{n − 1}, …, a₁) the type of 𝒫. In this article we identify all 8‐tuples (a₈, a₇, …, a₂, 0) that are the types of partitions of V(8, 2). © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 462–474, 2010