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Decoding of Binary Information and Error Correction (III)

See the attached file.

Consider the (3,8) encoding function  e:B^3 --> B^8  defined by  

 e(000) = 00000000  
 e(001) = 10111000
 e(010) = 00101101  
 e(011) = 10010101  
 e(100) = 10100100 
 e(101) = 10001001  
 e(110) = 00011100  
 e(111) = 00110001  
 and these are code words.  

Let d be an (8,3) maximum likelihood decoding function  d:B^8  --> B^3  associated with e. How many errors can (e,d) correct?  
The complete problem is in the file.


Solution Preview

We have to show that the set of code words  
 N = {00000000, 10111000, 00101101, ...

Solution Summary

This solution explains the problems of decoding of the binary informations and error correction. The solution is given in detail.  
This is mainly for solving the problem of transmission of data and that of receiving the data in computer science.