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Universal Gröbner bases for binary linear codes
Publikationstyp
Journal Article
Date Issued
2013
Sprache
English
Author(s)
Institut
TORE-URI
Volume
86
Issue
2
Start Page
345
End Page
358
Citation
International Journal of Pure and Applied Mathematics 2 (86): 345-358 (2013)
Publisher DOI
Scopus ID
Publisher
Academic Publishing
Each linear code can be described by a code ideal given as the sum of a toric ideal and a non-prime ideal. In this way, several concepts from the theory of toric ideals can be translated into the setting of code ideals. It will be shown that after adjusting some of these concepts, the same inclusion relationship between the set of circuits, the universal Gröbner basis and the Graver basis holds. Furthermore, in the case of binary linear codes, the universal Gröbner basis will consist of all binomials which correspond to codewords that satisfy the Singleton bound and a particular rank condition. This will give rise to a new class of binary linear codes denoted as Singleton codes. © 2013 Academic Publications, Ltd.
Subjects
linear code
Gröbner basis
universal Gröbner basis
Graver basis
circuit
toric ideal
Singleton code
DDC Class
510: Mathematik