Permutation Polynomials Modulo Q·p~w And Latin Squares Over Them

This paper studies permutation polynomials modulo q·pw (p= 2,3,5) and Latin squares over them, obtains the following results:(1) Characterizing a poly-nomial represents a permutation polynomial modulo 5w, only deal with coefficients of the polynomial. (2) Proving that a binary polynomial formed a Latin square over5w, if and only if all ten polynomials:p(x,i),p(i,y),(i=0,1,2,3,4.) are permutation polyno-mials modulo 5w. (3) Pointing out that not all Latin squares formed by permutation po-lynomials modulo 3w are orthogonal Latin squares; and giving some sufficient condi-tions that they are orthogonal.