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

THE EQUIVALENT IDENTITIES OF THE MACWILLIAMS IDENTITIES FOR LINEAR CODES

2015 ◽  
Vol 76 (1) ◽  
Author(s):  
Bao Xiaomin
Keyword(s):  
Linear Codes ◽  
Macwilliams Identity ◽  
Macwilliams Identities

We use derivatives to prove the equivalences between MacWilliams identity and its four equivalent forms, and present new interpretations for the four equivalent forms.

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.

scholarly journals Character sums and MacWilliams identities

2004 ◽  
Vol 287 (1-3) ◽  
pp. 155-160 ◽  
Author(s):  
Dae San Kim ◽  
Dong Chan Kim
Keyword(s):  
Character Sums ◽  
Macwilliams Identities
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