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Write down a generator matrix for the cyclic code C of length 8 over F3...

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Accounting

Write down a generator matrix for the cyclic code C of length 8 over F3 with generator polynomial g(x) = x^3 + 2x^2 + 2. What is the dimension of C over F3?

Compute the parity check polynomial for C. Hence write down a parity check matrix for C over F3.

Determine the roots of g(x) in F9. Hence write down the designed distance of C as a BCH code over F3. What is the actual minimum distance of C?

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