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

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Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6.
Bayreuth , 2017 . - 16 S.

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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 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 also 257.