We pose x = (101101) and y = (011110). Calculate d _H( x,y), w _H( X) and w _H( y).

Perform the following operations:

1. build B _p( X) with ? = 2 and x = (10111);

2. build B ₁( X) ? B ₂( y) with x = (110111), y = (000110);

3. give the parameters of the following binary code:

   
   

4. give the parameters of the following ternary code:

   
   

5. construct a binary code of length 5 with the largest possible cardinal that corrects 2 errors per word;

6. construct a binary code of length 7 with the largest possible cardinal that corrects 1 error per word.

Let there be a binary code of length n with a cardinal M. What is the volume of memory necessary to make a table decoding using class representatives (in a number of binary positions)?

How many elements are there in a sphere of radius r included in

Let there be a binary code C of length n and cardinal M. Prove that the greatest error correcting capability of the code is the largest integer r such that we have , where is the number of combinations of i objects from n.