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Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6. (English) Zbl 1409.51010

Summary: 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.

MSC:

51E23 Spreads and packing problems in finite geometry
94B65 Bounds on codes
05B25 Combinatorial aspects of finite geometries
90C05 Linear programming
90C10 Integer programming

Software:

Cliquer; CPLEX
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References:

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