2017/03/25 by Daniel Heinlein, Heinlein, Daniel, Sascha Kurz +1
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1703.08712
openalex publication_date 2017/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that the maximum size A2(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 A2(8,6;4)≤ 289 was implied by the Johnson bound and the maximum size A2(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.