The encoding function E: Z22 Z52 is given by the generator matrix (a) Determine all code words.

Question:

The encoding function E: Z22 †’ Z52 is given by the generator matrix

(a) Determine all code words. What can we say about the error-detection capability of this code? What about its error- correction capability?
(b) Find the associated parity-check matrix H.
(c) Use H to decode each of the following received words,
(i) 11011
(ii) 10101
(iii) 11010
(iv) 00111
(v) 11101
(vi) 00110