4023f11ps7

4023f11ps7 - G = 2 4 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1...

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Homework #7 Due: October 26, 2011 1. Let C ( F 2 ) 9 be the subset C = ' abcabc a b c j a; b; c 2 F 2 ; where x is 1 if x is 0 and x is 0 if x is 1. Then C is a binary code of length 9. (a) List all of the codewords in C . (b) Show that C is not a linear code. (c) How many errors does C detect and how many errors does it correct. 2. Determine the generator matrix, all codewords, and the dual code of the [4 ; 2] code over F 3 with parity check matrix H = 1 1 1 0 1 2 0 1 : 3. Let C be the ternary linear code with generator matrix G = 1 0 2 2 0 0 1 1 0 1 : List all the codewords in C and flnd the weight of each codeword. What is the minimum distance d ( C )? 4. Let C be a binary [7 ; 3] code with generator matrix
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Unformatted text preview: G = 2 4 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 3 5 : Show that C is self-orthogonal. Find its dual code. 5. Nagpaul-Jain, Page 183, #21. 6. Construct a standard array for the [5 ; 2] binary code with generator matrix G = 1 0 1 1 0 0 1 0 1 1 : Use your array to decode the received vectors 11101 and 01001. 7. Let C be the [5 ; 3] ternary code with parity check matrix H = 1 0 1 1 0 2 2 1 0 1 : Construct a syndrome table for C and use your table to decode the received strings 11202 and 20201. Math 4023 1...
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