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hw3_810

# hw3_810 - are nonzero and distinct Additionally assume that...

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Math 810, Spring 2011 – HW 3 Due Wednesday, 2 March 2011 1. ( a ) Give a syndrome table (syndrome dictionary) for the [9 , 5] binary linear code E with the following check matrix: 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 . ( b ) Use your table to decode the received word: (0 , 1 , 0 , 1 , 1 , 0 , 0 , 0 , 0) . ( c ) Use your table to decode the received word: (1 , 1 , 1 , 0 , 1 , 1 , 0 , 1 , 0) . 2. Let H be a check matrix for the binary linear code C . Assume that the columns of H are nonzero and distinct. Additionally assume that each column
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Unformatted text preview: are nonzero and distinct. Additionally assume that each column of H contains an odd number of 1’s. Prove that d min ( C ) ≥ 4. 3. Let D be a linear ternary code (that is, a linear code over F 3 ). Prove that either all of the codewords begin with 0 or exactly 1 / 3 of the codewords begin with 0....
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