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In this thesis we related the notion on constructions of irreducible polynomials over finite fields. A polynomial with integer coefficients or more generally, with coefficients in a unique factorization domain is sometimes said to be irreducible if it is an irreducible element of the polynomial ring. That is, not invertible, not zero and cannot be factored into the product of two non-invertible polynomials with coefficients. The estimates for the preprocessing time depend on unproven conjectures.