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Asymptotic bounds for the sizes of constant dimension codes and an improved lower bound

URN to cite this document: urn:nbn:de:bvb:703-epub-3298-6

Title data

Heinlein, Daniel ; Kurz, Sascha:
Asymptotic bounds for the sizes of constant dimension codes and an improved lower bound.
Bayreuth , 2017 . - 30 S.

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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

We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show relations between them. A slightly improved version of the so-called linkage construction is presented which is e.g. used to construct constant dimension codes with subspace distance d=4, dimension k=3 of the codewords for all field sizes q, and sufficiently large dimensions v of the ambient space, that exceed the MRD bound, for codes containing a lifted MRD code, by Etzion and Silberstein.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen in:
Barbero, Ángela I. ; Skachek, Vitaly ; Ytrehus, Øyvind (Hrsg.): Coding Theory and Applications : 5th International Castle Meeting, ICMCTA 2017, Vihula, Estonia, August 28-31, 2017, Proceedings. - Cham : Springer International Publishing , 2017 . - S. 163-191 . - (Lecture Notes in Computer Science ; 10495)
ISBN 9783319662787
DOI: https://doi.org/10.1007/978-3-319-66278-7_15
Keywords: constant dimension codes; subspace distance; injection distance; random network coding
Subject classification: Mathematics Subject Classification Code: 51E23 05B40 (11T71 94B25)
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3298-6
Date Deposited: 11 May 2017 09:12
Last Modified: 27 May 2021 08:29
URI: https://epub.uni-bayreuth.de/id/eprint/3298

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