# Soln06 - ECE 342 Communication Theory Fall 2005, Solutions...

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Unformatted text preview: ECE 342 Communication Theory Fall 2005, Solutions to Homework 6 Prof. Tiffany J Li www: http://www.eecs.lehigh.edu/ jingli/teach email: jingli@ece.lehigh.edu Problem 9.22 The codewords of the linear code of Example 9.5.1 are c 1 = [ 0 0 ] c 2 = [ 1 1 0 ] c 3 = [ 0 1 1 1 1 ] c 4 = [ 1 1 1 1 ] Since the code is linear the minimum distance of the code is equal to the minimum weight of the codewords. Thus, d min = w min = 2 There is only one codeword with weight equal to 2 and this is c 2 . Problem 9.25 The parity check matrix H of the (15,11) Hamming code consists of all binary sequences of length 4, except the all zero sequence. The systematic form of the matrix H is H = [ P t | I 4 ] = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 The corresponding generator matrix is G = [ I 11 | P ] = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1...
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## This note was uploaded on 08/06/2008 for the course ECE 342 taught by Professor Li during the Fall '05 term at Lehigh University .

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Soln06 - ECE 342 Communication Theory Fall 2005, Solutions...

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