Consider the following table: Define a (4, 8) block code as follows: Encode the...

Consider the following table:

Define a (4, 8) block code as follows: Encode the message word as the code word where is chosen so that the number of 1s in the first row is even is chosen so that the number of 1s in the second row is even, is chosen so that the number of Is in the first column is even, and is chosen so that the number of is in the second column is even. Show that this code corrects all errors in a single digit.