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1252646244

# 1252646244 - n 1 Now consider the cyclic code of length n...

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ECE 635 Dr. N. El Naga Homework # 4 4.1 Let g(X) = 1 + X + X 2 + X 4 + X 5 + X 8 + X 10 be the generator polynomial of a (15,5) cyclic code. (a) Find the parity polynomial h(X) of this code. (b) Find the code polynomial for the message m(X) = 1 + X + X 4 (in systematic form). 4.2 Find the generator matrix and the parity check matrix for the code in Problem 1. 4.3 Let n be the smallest integer such that the polynomial g(X) divides X
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Unformatted text preview: n + 1. Now consider the cyclic code of length n which is generated by g(X). Show that this code has minimum weight at least 3. 4.4 Show that X + 1 is a factor of X n + 1. 4.5 Consider an (n,k) cycle code whose generator polynomial is g(X). Suppose that X + 1 is not a factor of g(X). Show that the vector of all 1's is a code vector....
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