2. Consider an (n,k) linear block code C that has odd minimum weight d. Let H...

    

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2. Consider an (n,k) linear block code C that has odd minimum weight d. Let H be the parity check matrix for the code C. Construct a new code C whose parity check matrix H is given as H = H 111. 0 0 0 0 1 that is, H is formed from H by adding one row of all 1's and one column of 0's ending in a 1. See if you can show the following about the code C. a. C, is an (n+1,k) code. b. Every code vector of C has even weight. c. The minimum weight codeword of C has weight d + 1. (Hint: The matrix H is key to showing these results.) 2. Consider an (n,k) linear block code C that has odd minimum weight d. Let H be the parity check matrix for the code C. Construct a new code C whose parity check matrix H is given as H = H 111. 0 0 0 0 1 that is, H is formed from H by adding one row of all 1's and one column of 0's ending in a 1. See if you can show the following about the code C. a. C, is an (n+1,k) code. b. Every code vector of C has even weight. c. The minimum weight codeword of C has weight d + 1. (Hint: The matrix H is key to showing these results.)