2. A parity check matrix H contains r rows and n columns. The columns of H...

  

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2. A parity check matrix H contains r rows and n columns. The columns of H have odd weight vectors of weight 1, 3, 5, etc. Note that n and r correspond to the length of the code and the number of check bits. For a given n the smallest r is chosen such that the total number of such column vectors is equal to n. (a) For n = 16 find the value of r and show the H matrix. (b) Show that this code is capable of correcting single errors and de- tecting double errors. (c) Find the corresponding G matrix. 2. A parity check matrix H contains r rows and n columns. The columns of H have odd weight vectors of weight 1, 3, 5, etc. Note that n and r correspond to the length of the code and the number of check bits. For a given n the smallest r is chosen such that the total number of such column vectors is equal to n. (a) For n = 16 find the value of r and show the H matrix. (b) Show that this code is capable of correcting single errors and de- tecting double errors. (c) Find the corresponding G matrix.

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a For n 16 we want to find the smallest r such that the total number of column vectors with odd weig... View the full answer