I am trying to generate a permutation of polynomial with order m Suppose m = 5 and N = 64. How do I choose the coefficients such that the polynomial is a permutation of nos from 0 to 63.?
I believe this is on topic. In general this is a math question and there are various permutation polynomial families, such as Dickson polynomials, see Wikipedia under "permutation polynomials". 

In the case $N=2^m$ (which seems to be the one you are interested in, though the term "order" instead of "degree" is problematic) there is a nice paper discussing such polynomials, by Ron Rivest entitled "Permutation polynomials modulo $2^w$ $w\geq 1.$ I state the main result.

$P(x)=a_0+a_1x+\cdots+a_d x^d$ over the integers modulo $2^w$ is a permutation polynomial if and only if $a_1$ is odd, $a_2+a_4+a_6+\cdots$ is even, and $a_3+a_5+a_7+\cdots$ is even.

See the paper for more related results, e.g., on polynomials generating latin squares mod $2^w$, just google "Rivest permutation polynomial".