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

Titelangaben

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Optimal binary subspace codes of length 6, constant dimension 3 and minimum subspace distance 4.
In: Kyureghyan, Gohar ; Mullen, Gary L. ; Pott, Alexander (Hrsg.): Topics in Finite Fields. - Providence, Rhode Island : American Mathematical Society , 2015 . - S. 157-176 . - (Contemporary Mathematics ; 632 )
ISBN 978-0-8218-9860-4
DOI: https://doi.org/10.1090/conm/632/12627

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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.