An upper bound for binary subspace codes of length 8, constant dimension 4 and minimum distance 6

Titelangaben

Heinlein, Daniel ; Kurz, Sascha:
An upper bound for binary subspace codes of length 8, constant dimension 4 and minimum distance 6.
In: Augot, Daniel ; Krouk, Evgeny ; Loidreau, Pierre (Hrsg.): The Tenth International Workshop on Coding and Cryptography 2017 : WCC Proceedings. - Saint-Petersburg , 2017

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Abstract

It is shown that the maximum size A_2(8,6;4) of a binary subspace code of packet length v=8, minimum subspace distance d=4, and constant dimension k=4 is at most 272. In Finite Geometry terms, the maximum number of solids in PG(7,2), mutually intersecting in at most a point, is at most 272. Previously, the best known upper bound A_2(8,6;4)<= 289 was implied by the Johnson bound and the maximum size A_2(7,6;3)=17 of partial plane spreads in PG(6,2). The result was obtained by combining the classification of subspace codes with parameters (7,17,6;3)_2 and (7,34,5;{3,4})_2 with integer linear programming techniques. The classification of (7,33,5;{3,4})_2 subspace codes is obtained as a byproduct.