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

摘要

We determine the maximum size A2(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 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 A2(8,6) of a binary mixed-dimension subspace code of packet length 8 and minimum subspace distance6 is 257 as well.