Carleton University
Technical Report TR-221
March 1993
Note on Systems of Polynomial Equations over Finite Fields
Vincenzo Acciaro
Abstract
Let F be a finite field of q elements and characteristic p ( so q = pn for some n 1) and let r := {Ji(x1, … ,xr) = Oli = 1, … ,s} be a system of polynomial equations with coefficients in F.
In this paper we relate the structure of the F-algebra
F[x1, … , Xr]/(fi(x1, … , Xr), … , fa(X1, … ,xr), x1 – X1, … , xi – Xr) to the roots of r in pr.