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arXiv · 2105.01584

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

Anirban Ghatak·Sumanta Mukherjee
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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.

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Anirban Ghatak, Sumanta Mukherjee. 2021-05-04. Intersection Patterns in Optimal Binary $(5,3)$ Doubling Subspace Codes. https://arxiv.org/abs/2105.01584

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