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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.
Bd. 87
(2019)
Heft 2-3
.
- S. 375-391.
ISSN 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0544-8
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| Projekttitel: |
Offizieller Projekttitel Projekt-ID Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche Geometrie Ohne Angabe |
|---|---|
| Projektfinanzierung: |
Deutsche Forschungsgemeinschaft |
Abstract
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.