Determine a generator matrix
Solve the following problem:
The polynomial
g(X) = X4 + X + 1
is the generator for the (15, 11) Hamming binary code.
a. Determine a generator matrix G for this code in systematic form.
b. Determine the generator polynomial for the dual code.
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The following table shows the current relationship between bond ratings and default risk premiums:
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For the (7, 4) cyclic Hamming code with generator polynomial g(X) = X3 + X2 + 1, construct an (8, 4) extended Hamming code .
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Determine a generator matrix G for this code in systematic form.
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