1252646241 - Find the roots of : f(x) = 1 + x 2 + x 3 over...

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ECE 635 Dr. N. El Naga Homework #1 1. Solve the following simultaneous equations of X,Y,Z, and W with modulo-2 arithmetic: X + Y + W = 1, X + Z + W = 0, X + Y + Z + W = 1, Y + Z + W = 0. 2. Show that X 5 + X 3 + 1 is irreducible over GF(2). 3. Find all the irreducible polynomials of degree 5 over GF (2). 4. (a) Construct a table for GF(2 3 ) based on the primitive polynomial p(X) = 1 + X + X 3 . (b) Display the power, polynomial, and vector representations of each element. (c) Determine the order of each element. (d)
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Unformatted text preview: Find the roots of : f(x) = 1 + x 2 + x 3 over the above GF(2 3 ). 5. A storage system has the following media characteristics: 1. Probability of no-error = .6 2. Probability of 1-bit error = .25 3. Probability of 2-bit error = .1 4. Probability of more than 2-bit error = .05 What will be the probability of error in the retrieved data in each of the following cases: a) If no error correcting code is used ? b) If a 1-bit error correcting code is used ? c) If a 2-bit error correcting code is used ?...
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