Title data
Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6.
In: Designs, Codes and Cryptography.
Vol. 87
(2019)
Issue 2-3
.
- pp. 375-391.
ISSN 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0544-8
Related URLs
Project information
Project title: |
Project's official title Project's id Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche Geometrie No information |
---|---|
Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract in another language
The maximum size A_2(8,6;4) of a binary subspace code of packet length v=8, minimum subspace distance
d=6, and constant dimension k=4 is 257, where the 2 isomorphism types are extended lifted maximum rank distance codes. In Finite Geometry terms the maximum number of solids in PG(7,2), mutually intersecting in at most a point, is 257. The result was obtained by combining the classification of substructures with integer linear programming techniques.
This implies that the maximum size A_2(8,6) of a binary mixed-dimension code of packet length 8 and minimum subspace distance 6 is also 257.