Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6

Abstract

The maximum size $A_2(8,6;4)$ of a binary subspace code of packet length $v=8$, minimum subspace distance $d=6$, and constant dimension $k=4$ is $257$, where the $2$ isomorphism types are extended lifted maximum rank distance codes. In finite geometry terms the maximum number of solids in $\mathrm{PG}(7,2)$, mutually intersecting in at most a point, is $257$. The result was obtained by combining the classification of substructures with integer linear programming techniques. This implies that the maximum size $A_2(8,6)$ of a binary mixed-dimension code of packet length $8$ and minimum subspace distance $6$ is $257$ as well.

17 pages, 3 tables

References in corpus (1)

• Improved upper bounds for partial spreads

Cited by in corpus (4)

• On the lengths of divisible codes
• Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects
• Subspace Packings -- Constructions and Bounds
• Subspaces intersecting in at most a point