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

TL;DR

This paper investigates the intersection patterns of subspaces in optimal binary (5,3) doubling subspace codes, providing a new characterization of a subclass based on these patterns and classifying spread types in specific code constructions.

Contribution

It introduces a new characterization of binary doubling codes through intersection patterns and classifies spread types in optimal code constructions over GF(2).

Findings

Classified types of spreads in doubling codes from recent constructions.

Established intersection pattern-based characterization of a binary doubling code subclass.

Utilized complete classification of maximal partial line spreads in PG(4,2).

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.