A class of polynomials

Abstract

Then 41(t) has the linearity properties (1.3) i1/(t + U) = 74 (t) + /f(U) V l) (Ct) =CV (t) for arbitrary c in GF(pn); further from (1.2) it follows that (1 .4) AV(xt) = Vlpn(t) XVI'(t). In turn (1.4) implies the general relation (1.5) (1) M7/,(Mt) = CWM(NI(t)), where M is a polynomial in GF(pn) of degree m in x, and m (_ 1')m j (1.6) <M(U) = / j(M)p i=o Fj It remains to define j/'(t). We put