Optimal binary subspace codes of length 6, constant dimension 3 and minimum distance 4

Titelangaben

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Optimal binary subspace codes of length 6, constant dimension 3 and minimum distance 4.
Bayreuth , 2014 . - 24 S.

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Abstract

It is shown that the maximum size of a binary subspace code of packet length v=6, minimum subspace distance d=4, and constant dimension k=3 is M=77; in Finite Geometry terms, the maximum number of planes in PG(5,2) mutually intersecting in at most a point is 77. Optimal binary (v,M,d;k)=(6,77,4;3) subspace codes are classified into 5 isomorphism types, and a computer-free construction of one isomorphism type is provided. The construction uses both geometry and finite fields theory and generalizes to any q, yielding a new family of q-ary (6,q^6+2q^2+2q+1,4;3) subspace codes.