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

Abstract

Subspace codes are collections of subspaces of a projective space such that any two subspaces satisfy a pairwise minimum distance criterion. There exists a significant body of research on subspace codes, especially with regard to their application for error and erasure correction in random networks. 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 fields F q , termed doubling codes. In this context, 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 doubling codes based on the intersection patterns of key subspaces in the pair of constituent spreads. This characterization is a first step towards identifying all possible spread pairs that can yield optimal (5, 3) 2 doubling codes.