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# hmwk6 - u = x Note the polynomial g x is in GF(16 x not...

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Math 523 Homework 6 Due 5:30 pm 7/31/2008 Total: 30 points From Chapter 4 of the text: 4.1. Construct a generator polynomial for a 3-error correcting Reed-Solomon code of length 10 over Z 11 . 4.2. Construct a [4 , 2] Reed-Solomon code C over Z 5 . That is, find a generator polynomial for C , a generator matrix for C , and list the elements of C . Find the minimum distance of C ; how many errors will it correct? 4.5. Find a generator polynomial g ( x ) for a [15 , 11] Reed-Solomon code over GF(16). Use Z 2 [ x ] / x 4 + x + 1 as your representation of GF(16), and use the primitive root
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Unformatted text preview: u = [ x ]. Note: the polynomial g ( x ) is in GF(16)[ x ], not necessarily Z 2 [ x ]. Additional problems: 1. Construct a [15 , k ] BCH code over Z 2 with designed distance 5 for which k is as large as possible. What is the minimum distance of the code? 2. Construct a [15 , k ] BCH code over Z 2 with designed distance 7 for which k is as large as possible. What is the minimum distance of the code? 3. Construct a BCH code of length 8 over Z 3 with designed distance 5....
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