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Bounds for the multilevel construction

Title data

Feng, Tao ; Kurz, Sascha ; Liu, Shuangqing:
Bounds for the multilevel construction.
Bayreuth , 2020 . - 95 p.
DOI: https://doi.org/10.15495/EPub_UBT_00005161

Official URL: Volltext

Abstract in another language

One of the main problems in random network coding is to compute good lower and upper bounds on the achievable cardinality of the so-called subspace codes in the rojective space PG(n,q) for a given minimum distance. The determination of the exact maximum cardinality is a very tough discrete optimization problem involving a huge number of symmetries. Besides some explicit constructions for good subspace codes several of the most successfull constructions involve the solution of discrete optimization subproblems itself, which mostly have not been not been solved systematically. Here we consider the multilevel a.k.a. Echelon--Ferrers construction and given lower and upper bounds for the achievable cardinalities. From a more general point of view, we solve maximum clique problems in weighted graphs, where the weights can be polynomials in the field size of size q.

Further data

Item Type: Preprint, postprint
Keywords: Galois geometry; partial spreads; constant--dimension codes; subspace codes; subspace distance; Echelon-Ferrers construction; multilevel construction
Subject classification: Mathematics Subject Classification Code: 51E23 (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: 21 Nov 2020 22:00
Last Modified: 23 Nov 2020 07:55
URI: https://eref.uni-bayreuth.de/id/eprint/60250