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New Lower Bounds for Binary Constant-Dimension Subspace Codes

ABSTRACT Let denote the maximum cardinality of a set of k-dimensional subspaces of an n-dimensional vector space over the finite field of order q, , such that any two different subspaces have a distance of at least d. Lower bounds on can be obtained by explicitly constructing corresponding sets . 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 . With a stochastic maximum weight clique algorithm and a systematic consideration of groups of the above mentioned type, new lower bounds on and for 8 ⩽ n ⩽ 11 are obtained.