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

Title data

Kurz, Sascha:
The interplay of different metrics for the construction of constant dimension codes.
Bayreuth , 2021 . - 18 p.
DOI: https://doi.org/10.15495/EPub_UBT_00005780

Official URL:

Abstract in another language

A basic problem for constant dimension codes is to determine the maximum possible size A_q(n,d;k) of a set of k-dimensional subspaces in GF(q)ⁿ, 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_q(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_q(10,4;5), A_q(11,4;4), A_q(12,6;6), and A_q(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)
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
Result of work at the UBT:	Yes
DDC Subjects:	000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics
Date Deposited:	25 Sep 2021 21:00
Last Modified:	27 Sep 2021 07:45
URI:	https://eref.uni-bayreuth.de/id/eprint/67111