Linearized polynomials are useful in the study of polynomial factorization techniques because they have enough structure to allow an easy procedure to find their roots.
DEFINITION 8.1 Over GF(qm), a linearized polynomial (or a q-poly- nomial) is defined as a polynomial of the form
with coefficients in the extension field GF(qm) of GF(q).
Let F be an arbitrary extension of GF(qm).
THEOREM 8.2 Let , then it follows that
(a) Property 1:
(b) Property 2:
■ Property 1.