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 · EPub Bayreuth (University of Bayreuth) · 2017
We determine 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 $$k=4$$ to be 257. There are two isomorphism types of optimal codes. Both of them are extended LMRD codes. In finite geometry terms, the maximum number of solids in $${\text {PG}}(7,2)$$ 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 result implies that the maximum size $$A_2(8,6)$$ of a binary mixed-dimension subspace code of packet length 8 and minimum subspace distance 6 is 257 as well.