Nonlinear Codes for Test Patterns Compression: The Old School Way

2021 ◽  
pp. 125-142
Author(s):  
Jan Schmidt ◽  
Petr Fišer
Keyword(s):  
Nonlinear Codes

The MacWilliams Identities for Nonlinear Codes

1972 ◽  
Vol 51 (4) ◽  
pp. 803-819 ◽  
Author(s):  
F. J. MacWilliams ◽  
N. J. A. Sloane ◽  
J.-M. Goethals
Keyword(s):  
Macwilliams Identities ◽  
Nonlinear Codes

Generating nonlinear codes for multi-bit symbol error correction using cellular automata

2021 ◽  
Vol 415 ◽  
pp. 132758
Author(s):  
Swapan Maiti ◽  
Meghna Sengupta ◽  
Dipanwita Roy Chowdhury
Keyword(s):  
Cellular Automata ◽  
Error Correction ◽  
Nonlinear Codes

scholarly journals COMPUTING THE DISTANCE DISTRIBUTION OF SYSTEMATIC NONLINEAR CODES

2010 ◽  
Vol 09 (02) ◽  
pp. 241-256 ◽  
Author(s):  
ELEONORA GUERRINI ◽  
EMMANUELA ORSINI ◽  
MASSIMILIANO SALA
Keyword(s):  
Weight Distribution ◽  
Gröbner Basis ◽  
Black Box ◽  
Distance Distribution ◽  
The Other ◽  
Brute Force ◽  
Grobner Basis ◽  
Other Hand ◽  
Closest Pair ◽  
Nonlinear Codes

The 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.

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