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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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This note was uploaded on 02/27/2010 for the course ECE 635 taught by Professor Profnaganagi during the Spring '09 term at CSU Northridge.
 Spring '09
 profnaganagi

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