Determine whether the following polynomials are generator
polynomials of cyclic codes of given lengths:

(1) g(x) = 1 + x + x^{2} + x^{3} + x^{4}
for a binary cyclic code of length 7;

(2) g(x) = 2 + 2x^{2} + x^{3} for a ternary cyclic
code of length 8.

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