New Lower Bounds for Binary Constant-Dimension Subspace Codes

Let (Formula presented.) denote the maximum cardinality of a set (Formula presented.) of k-dimensional subspaces of an n-dimensional vector space over the finite field of order q, (Formula presented.), such that any two different subspaces (Formula presented.) have a distance (Formula presented.) of at least d. Lower bounds on (Formula presented.) can be obtained by explicitly constructing corresponding sets (Formula presented.). When searching for such sets with a prescribed group of automorphisms, the search problem leads to instances of the maximum weight clique problem. The main focus is here on subgroups with small index in the normalizer of a Singer subgroup of (Formula presented.). With a stochastic maximum weight clique algorithm and a systematic consideration of groups of the above mentioned type, new lower bounds on (Formula presented.) and (Formula presented.) for 8 ⩽ n ⩽ 11 are obtained.