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ass210 - Copy - University of Victoria Department of...

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University of Victoria Department of Electrical and Computer Engineering ELEC 511 Error Control Coding Techniques in Communications 2010 Assignment 2 1. Consider the set of binary vectors of length 6. a) Is it possible to find eight vectors with minimum Hamming distance 3? b) Is it possible to find nine vectors with minimum Hamming distance 3? 2. Construct a standard array for the ternary Hamming [4,2,3] code. 3. Let C be a binary linear [ n,k,d ] code with generator matrix G . We may assume that the first row of G has the form 1 · · · 10 · · · 0, so that G = bracketleftBigg 1 · · · 1 0 · · · 0 G 1 G 2 bracketrightBigg . Let d 2 be the minimum distance of the [ n - d,k - 1] code with generator matrix G 2 . Show that d 2 d/ 2. 4. If a binary linear code C has parity check matrix H , what is the parity check matrix of the extended code C obtained by adding an overall parity check to each codeword. 5. Devise a single error correcting code for the 7-bit ASCII character set.
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