A Class of Polynomials*

  title={A Class of Polynomials*},
  author={L. Carlitz},
00 (— l)k (1.2) m-Y,}L-rLt**, k=0 r k where t takes on the values 00 t = £ cm_¡xm-' (cj in GF(p»)). j'-o Then \p(t) has the linearity properties (1.3) W + u) m + *(u), Hct) = ok(t), for arbitrary c in GF(pH); further from (1.2) it follows that (1.4) ik(xt) = ^"(t) x^(t). In turn (1.4) implies the general relation (1.5) (l)^(Mt) =«*(*(*)), where M is a polynomial in GF(pn) of degree m in x, and