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arXiv · 1711.06624

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

Daniel Heinlein·Thomas Honold·Michael Kiermaier·Sascha Kurz·Alfred Wassermann
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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 $\operatorname{PG}(7,2)$, 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.

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Daniel Heinlein, Thomas Honold, Michael Kiermaier, Sascha Kurz, Alfred Wassermann. 2018-10-20. Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6. https://doi.org/10.1007/s10623-018-0544-8

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