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TitleGr\"obner bases for perfect binary linear codes.
Author(s) Natalia Dück, Karl-Heinz Zimmermann
TypeArticle in Journal
AbstractThere is a deep connection between linear codes and combinatorial designs. Combinatorial designs can give rise to linear codes and vice versa. In particular, perfect codes always hold combinatorial designs. Recently, linear codes have been associated to binomial ideals by the so-called code ideal which completely describes the code. It will be shown that for a perfect binary linear code, the codewords of minimum Hamming weight are in one-to-one correspondence with the elements of a reduced Gröbner basis for the code ideal with respect to any graded order.
KeywordsGröbner basis, linear code, perfect code, Steiner system, minimum distance
ISSN1311-8080; 1314-3395/e
File
URL http://ijpam.eu/contents/2014-91-2/2/index.html
LanguageEnglish
JournalInt. J. Pure Appl. Math.
Volume91
Number2
Pages155--167
PublisherAcademic Publications, Sofia
Year2014
Edition0
Translation No
Refereed No
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