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.
In: Advances in Mathematics of Communications. Vol. 17 (2023) Issue 1 . - pp. 152-171.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2021069

Official URL:

Abstract in another language

A basic problem for constant dimension codes is to determine the maximum possible size Aq(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 Aq(10,4;5), Aq(11,4;4), Aq(12,6;6), and Aq(15,4;4). We also derive general upper bounds for subcodes arising in those constructions.

Further data

Item Type:	Article in a journal
Refereed:	Yes
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 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
Result of work at the UBT:	Yes
DDC Subjects:	000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics
Date Deposited:	22 Dec 2022 06:31
Last Modified:	22 Dec 2022 06:31
URI:	https://eref.uni-bayreuth.de/id/eprint/73184