Two classes of permutation polynomials over finite fields

Two new classes of permutation polynomials over finite fields are presented: (i) f(x)=(1-x-x^2)x^3^^^e^+^1^2-1-x+x^2 over F"3"^"e where e is a positive even integer; (ii) g"n","p(x)=@?"n"p"=<"l"=<"n"p"-"1nl(ln-l(p-1))xx^n^-^l^(^p^-^1^) over F"p"^"e where e is a positive integer such that e=0(mod 2) if p=2, and n=(p-1)p^m+p^0^e+p^1^e+...+p^(^p^-^1^)^e, (m-1,e)=1. The permutation polynomial in (i) answers an open question about reversed Dickson polynomials.