Factorizations of root-based polynomial compositions

  title={Factorizations of root-based polynomial compositions},
  author={Donald Mills},
  journal={Discrete Mathematics},
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