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# Decoding of Binary Information and Error Correction (VI)

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

e(000) = 00000000
e(001) = 01110010
e(010) = 10011100
e(011) = 01110001
e(100) = 01100101
e(101) = 10110000
e(110) = 11110000
e(111) = 00001111                         and these are code words.

Let d be an (8,3) maximum likelihood decoding function  d:B^8 --> B^3       associated with e.

Determine the number of errors that (e,d) will correct.

The complete problem is in the attached file

#### Solution Preview

The solution of the problem is in the attached file.

Decoding of Binary Information and Error Correction (VI)
By:- Thokchom Sarojkumar Sinha

Consider the (3,8) encoding function defined by
e(000) = 00000000
e(001) = 01110010
e(010) = 10011100
e(011) = 01110001
e(100) = 01100101
e(101) = 10110000
e(110) = 11110000
e(111) = 00001111

and these are code words.
Let d be an (8,3) maximum likelihood decoding function
associated with e.
Determine the number of errors that (e,d) will correct.

Solution:- The minimum distance of the function e can be checked by computing
the minimum of the distances between all i.e., distinct pairs
of code words.
Finding the distances with the identity is obvious.
For
...

#### 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.

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