Title  Computing the distance distribution of systematic nonlinear codes. 
Author(s)  Eleonora Guerrini, Emmanuela Orsini, Massimiliano Sala 
Type  Article in Journal 
Abstract  The most important families of nonlinear codes are systematic. A bruteforce 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 blackbox complexity model, the check is optimal among closestpair 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.

Keywords  Gröbner basis; distance distribution; Hamming distance; nonlinear code 
ISSN  02194988 
URL 
http://www.worldscientific.com/doi/abs/10.1142/S0219498810003884 
Language  English 
Journal  J. Algebra Appl. 
Volume  9 
Number  2 
Pages  241256 
Publisher  World Scientific, Singapore 
Year  2010 
Edition  0 
Translation 
No 
Refereed 
No 