A survey of the different types of vector space partitions (Q2905300)

A vector space partition is a collection \(\mathcal P\) of subspaces of a (finite) vector space such that each non-zero vector is contained in precisely one element of \(\mathcal P\). The author points out relations of vector space partitions to finite projective planes, design theory and the theory of error correcting codes.NEWLINENEWLINEA vector space partition is of type \([d_ 1^{n_ 1} \dots d_ t^{n_ t}]\) if it contains precisely \(n_ i\) subspaces of dimension \(d_i\). The author surveys known results on the possible types of vector space partitions for vector spaces of dimension at most 8 over the field with 2 elements.