hw5_810_ss11

# hw5_810_ss11 - r =(4 3 2 1 7 10 Use Euclidean Algorithm...

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Math 810, Spring 2011 – HW 5 Due Friday, 15 April 2011 Make sure you justify your answers appropriately. For these problems, that means you should show your calculations in enough detail that I can follow them (and can try to locate any mistakes). Please do not do your calculations on a machine. As these problems are largely computational, I ask that you not collaborate on them. 1. As in Problem 2 of Homework 4, consider the code C = GRS 6 , 2 ( α , v ) over the ﬁeld F 11 of the integers modulo 11, where α = (1 , 2 , 4 , 8 , 5 , 10) and v = (1 , 1 , 1 , 1 , 1 , 1). ( a ) Give n , k , β , u with C = GRS n,k ( β , u ). ( b ) Again suppose a codeword has been transmitted and we receive the word
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Unformatted text preview: r = (4 , 3 , 2 , 1 , 7 , 10) . Use Euclidean Algorithm decoding to decode this received word. (If you do not end up with the same decoding as on HW4, then you have done something wrong.) 2. Problem 5.2.6 from the Notes . 3. Consider the code GRS 10 , 4 ( α , v ) over F 11 that was our classroom example. ( a ) Use Euclidean Algorithm decoding to decode the received vector (0 , 10 , 5 , 5 , 3 , 10 , , , 8 , 4) , ( b ) Use Euclidean Algorithm decoding to decode the received vector (0 , , , , , , 1 , 1 , 1 , 1) ....
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