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Constructions and bounds for mixed-dimension subspace codes

Title data

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Constructions and bounds for mixed-dimension subspace codes.
In: Advances in Mathematics of Communications. Vol. 10 (August 2016) Issue 3 . - pp. 649-682.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2016033

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Project information

Project title:
Project's official titleProject's id
Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche GeometrieNo information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. The resulting so-called Main Problem of Subspace Coding is to determine the maximum size A_q(v,d) of a code in PG(v−1,F_q) with minimum subspace distance d. Here we completely resolve this problem for d>=v−1. For d=v−2 we present some improved bounds and determine A_q(5,3)=2q^3+2 (all q), A_2(7,5)=34. We also provide an exposition of the known determination of A_q(v,2), and a table with exact results and bounds for the numbers A_2(v,d), v<=7.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Galois geometry; network coding; subspace code; partial spread
Subject classification: Mathematics Subject Classification Code: 94B05 05B25 51E20 (51E14 51E22 51E23)
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 II
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: 05 Oct 2016 11:09
Last Modified: 06 Oct 2016 05:56
URI: https://eref.uni-bayreuth.de/id/eprint/34825