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# Factorizations of root-based polynomial compositions

@article{Mills2001FactorizationsOR, title={Factorizations of root-based polynomial compositions}, author={Donald Mills}, journal={Discrete Mathematics}, year={2001}, volume={240}, pages={161-173} }

- Published 2001 in Discrete Mathematics
DOI:10.1016/S0012-365X(00)00389-7

Let Fq denote the nite eld of order q = p r , p a prime and r a positive integer, and let f(x) and g(x) denote monic polynomials in Fq x] of degrees m and n respectively. Brawley and Carlitz 1] introduce a general notion of root-based polynomial composition which they call the composed product and denote by f g. They prove that f g is irreducible over Fq if and only if f and g are irreducible with gcd(m; n) = 1. In this paper, we extend Brawley and Carlitz's work by examining polynomials which… CONTINUE READING