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 of V with exactly ai subspaces of dimension i for 1≤i≤n, we have , and we call the n-tuple (an, an − 1, …, a1) the type of . 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