Singleton codes

Publikationstyp
Journal Article
Date Issued
2014
Sprache
English
Author(s)
Dück, Natalia  
Zimmermann, Karl-Heinz  
Institut
Eingebettete Systeme E-13  
TORE-URI
http://hdl.handle.net/11420/9925
Journal
International journal of pure and applied mathematics  
Volume
91
Issue
3
Start Page
273
End Page
290
Citation
International Journal of Pure and Applied Mathematics 91 (3): 273-290 (2014)
Publisher DOI
10.12732/ijpam.v91i3.1
Scopus ID
2-s2.0-84903383126
Publisher
Academic Publications
Each linear code can be described by a so-called code ideal. In order to utilize this ideal, Gröbner bases are required. Since many results depend on the chosen term order, knowledge of the universal Gröbner basis is advantageous. Singleton codes have the property that the universal Gröbner basis for their code ideals consists of all binomials associated to a codeword whose Hamming weight satisfies the Singleton bound. In this paper, properties of Singleton codes will be established and it will be examined which classical binary linear codes belong to the class of Singleton codes.
Subjects
Binary linear code
Circuit
Singleton bound
Singleton code
Universal Gröbner basis
DDC Class
004: Informatik
510: Mathematik