Intersection Patterns in Optimal Binary (5,3) Doubling Subspace Codes

05/04/2021

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by   Anirban Ghatak, et al.

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Subspace codes are collections of subspaces of a projective space such that any two subspaces satisfy a pairwise minimum distance criterion. Recent results have shown that it is possible to construct optimal (5,3) subspace codes from pairs of partial spreads in the projective space PG(4,q) over the finite field 𝔽_q, termed doubling codes. We have utilized a complete classification of maximal partial line spreads in PG(4,2) in literature to establish the types of the spreads in the doubling code instances obtained from two recent constructions of optimum (5,3)_q codes, restricted to 𝔽_2. Further we present a new characterization of a subclass of binary doubling codes based on the intersection patterns of key subspaces in the pair of constituent spreads.