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The interplay of different metrics for the construction of constant dimension codes

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005780
URN to cite this document: urn:nbn:de:bvb:703-epub-5780-8

Title data

Kurz, Sascha:
The interplay of different metrics for the construction of constant dimension codes.
Bayreuth , 2021 . - 18 S.

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Abstract

A basic problem for constant dimension codes is to determine the maximum possible size A<sub>q</sub>(n,d;k) of a set of k-dimensional subspaces in GF(q)<sup>n</sup>, called codewords, such that the subspace distance is at least d for all pairs of different codewords U, W. Constant dimension codes have applications in e.g. random linear network coding, cryptography, and distributed storage. Bounds for A<sub>q</sub>(n,d;k) are the topic of many recent research papers. Providing a general framework we survey many of the latest constructions and show up the potential for further improvements. As examples we give improved constructions for the cases A<sub>q</sub>(10,4;5), A<sub>q</sub>(11,4;4), A<sub>q</sub>(12,6;6), and A<sub>q</sub>(15,4;4). We also derive general upper bounds for subcodes arising in those constructions.

Further data

Item Type: Preprint, postprint
Keywords: Galois geometry; subspace distance; constant dimension codes; subspace codes; random linear 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-5780-8
Date Deposited: 23 Sep 2021 09:00
Last Modified: 23 Sep 2021 09:01
URI: https://epub.uni-bayreuth.de/id/eprint/5780

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