Geometrische Konstruktionen linearer Codes über Galois-Ringen der Charakteristik 4 von hoher homogener Minimaldistanz

URN to cite this document: urn:nbn:de:bvb:703-opus4-10320

Title data

Kiermaier, Michael:
Geometrische Konstruktionen linearer Codes über Galois-Ringen der Charakteristik 4 von hoher homogener Minimaldistanz.
Bayreuth , 2012 . - 103 S. P.
( Doctoral thesis, 2012 , University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

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Abstract

In dieser Arbeit werden vier neue unendliche Serien von linearen Codes über Galois-Ringen der Charakteristik 4 konstruiert. Hinsichtlich der Minimaldistanz übertreffen die Gray-Bilder der konstruierten Codes alle bekannten vergleichbaren linearen Codes. In den Konstruktionen wird die Theorie der projektiven Hjelmslev-Geometrien, der Assoziationsschemata sowie der symmetrischen Bilinearformen in endlichdimensionalen GF(2)-Vektorräumen benutzt.

Abstract in another language

In this thesis, four new infinite series of linear codes over Galois rings of characteristic 4 are constructed. In terms of the minimum distance, the Gray images of the constructed codes outperform all known comparable linear codes. For the constructions, the theory of projective Hjelmslev geometries, of association schemes and of symmetric bilinear forms in finite-dimensional GF(2)-vector spaces are used.

Further data

Item Type:	Doctoral thesis (No information)
Additional notes (visible to public):	msc: 05-XX; msc: 51-XX; msc: 94-XX; RVK: SK 170
Keywords:	endliche Geometrie; Ring <Mathematik>; Projektiver Hjelmslev-Raum; Hamming-Abstand; Assoziationsschema; ringlinearer Code; Galois-Ring; Kerdock-Code; Gray-Abbildung; homogenes Gewicht
DDC Subjects:	500 Science
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science
Language:	German
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-opus4-10320
Date Deposited:	25 Apr 2014 06:13
Last Modified:	25 Apr 2014 06:14
URI:	https://epub.uni-bayreuth.de/id/eprint/195

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