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Optimal Binary Subspace Codes of Length 6, Constant Dimension 3 and Minimum Subspace Distance 4
"... Abstract. It is shown that the maximum size of a binary sub-space code of packet length v = 6, minimum subspace distance d = 4, and constant dimension k = 3 is M = 77; in Finite Geom-etry terms, the maximum number of planes in PG(5; 2) mutually intersecting in at most a point is 77. Optimal binary ( ..."
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Abstract. It is shown that the maximum size of a binary sub-space code of packet length v = 6, minimum subspace distance d = 4, and constant dimension k = 3 is M = 77; in Finite Geom-etry 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 classied into 5 isomorphism types, and a computer-free construction of one isomorphism type is pro-vided. The construction uses both geometry and nite elds theory and generalizes to any q, yielding a new family of q-ary (6; q 6
