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. Recent results have shown that it is possible to construct optimal $(5,3)$ subspace codes from pairs of partial spreads in the projective space $\mathrm{PG}(4,q)$ over the finite field ${\mathbb{F}}_q$, termed doubling codes. We have utilized a complete classification of maximal partial line spreads in $\mathrm{PG}(4,2)$ 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 ${\mathbb{F}}_2$. 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.

19 pages, 1 figure