Give a small prime p  

Give a 2×2 matrix M with numbers in {0,...,p-1}, e.g.,  
[[1,1],[1,4]]

 

The permutation in the answer is a list 
of the images of 1,...,p²-1 under M.
Here, the nonzero vector [i,j] is identified with i+p(j-1), where i and j are taken to lie in {1,...,p} 
(so 0 is replaced by p).