15. Construct a binary linear code using all eight possible binary messages of length 3 and appending three check digits using the parity-check sums , and . Decode each of the received words below by the nearest-neighbor method:
001001, 011000, 000110, 100001
15.
000000, 100101, 010110, 001011, 110011, 101110, 011101, 111000. 001001 is decoded as 001011; 011000 is decoded as 111000; 000110 is decoded as 010110; 100001 is decoded as 100101.