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TitleComputing the distance distribution of systematic nonlinear codes.
Author(s) Eleonora Guerrini, Emmanuela Orsini, Massimiliano Sala
TypeArticle in Journal
AbstractThe most important families of nonlinear codes are systematic. A brute-force check is the only known method to compute their weight distribution and distance distribution. On the other hand, it outputs also all closest word pairs in the code. In the black-box complexity model, the check is optimal among closest-pair algorithms. In this paper, we provide a Gröbner basis technique to compute the weight/distance distribution of any systematic nonlinear code. Also our technique outputs all closest pairs. Unlike the check, our method can be extended to work on code families.

KeywordsGröbner basis; distance distribution; Hamming distance; nonlinear code
ISSN0219-4988
URL http://www.worldscientific.com/doi/abs/10.1142/S0219498810003884
LanguageEnglish
JournalJ. Algebra Appl.
Volume9
Number2
Pages241--256
PublisherWorld Scientific, Singapore
Year2010
Edition0
Translation No
Refereed No
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