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

Title data

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 (ed.): The Tenth International Workshop on Coding and Cryptography 2017 : WCC Proceedings. - Saint-Petersburg , 2017 . - 11 S.

Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
Integer Linear Programming Models for Subspace Codes and Finite GeometryNo information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type: Article in a book
Refereed: Yes
Keywords: subspace codes; network coding; constant dimension codes; subspace distance; integer linear programming; partial spreads
Subject classification: Mathematics Subject Classification Code: 51E23 05B40 (11T71 94B25)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 08 Dec 2017 07:46
Last Modified: 08 Dec 2017 07:46
URI: https://eref.uni-bayreuth.de/id/eprint/40888