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Coset Construction for Subspace Codes

Title data

Heinlein, Daniel ; Kurz, Sascha:
Coset Construction for Subspace Codes.
2016
Event: Network Coding and Designs , 4.-8.04.2016 , Dubrovnik, Kroatien.
(Conference item: Conference , Speech )

Related URLs

Project information

Project title:
Project's official titleProject's id
Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche GeometrieKU 2430/3-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

One of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable so-called subspace codes in PG$(n,q)$ for a given minimal distance. Here we generalize a construction of Etzion and Silberstein to a wide range of parameters. This construction, named coset construction, improves several of the previously best known subspace codes and attains the MRD bound for an infinite family of parameters:

Theorem:
For each $k\ge 4$ and arbitrary $q$ we have
$$
A_q(3k-3,2k-2;k)\ge q^{4k-6}+\frac{q^{2k-3}-q}{q^{k-2}-1}-q+1.
$$

and

Theorem:
$A_2(10,6;4)\ge 4173$.

Further data

Item Type: Conference item (Speech)
Refereed: No
Additional notes: Speaker: Daniel Heinlein
Keywords: Constant dimension codes; subspace codes; subspace distance;
Echelon-Ferrers construction
Subject classification: Mathematics Subject Classification Code: Primary 05B25, 51E20; Secondary 51E22, 51E23.
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 Mathematics in Economy
Faculties
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 18 Apr 2016 07:15
Last Modified: 30 Jun 2016 04:45
URI: https://eref.uni-bayreuth.de/id/eprint/32191