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Determine whether the following polynomials are generator polynomials of cyclic codes of given lengths: (1) g(x) = 1 + x + x 2 + x

Determine whether the following polynomials are generator polynomials of cyclic codes of given lengths: (1) g(x) = 1 + x + x2 + x3 + x4 for a binary cyclic code of length 7; (2) g(x) = 2 + 2x2 + x3 for a ternary cyclic code of length 8.

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