Thanks, Antonio. It looks very close to what I need, but I am getting some errors. For example, when I try for the addition table:

? addtable(2, x^3+x+1, x)
0       1       2       3       4       5       6       7       

1       2       4       7       2       6       5       3       

2       4       0       5       1       3       7       6       

3       7       5       0       6       2       4       1       

4       2       1       6       0       7       3       5       

5       6       3       2       7       0       1       4       

6       5       7       4       3       1       0       2       

7       3       6       1       5       4       2       0
[download]

The second entry on the second line is supposed to be 0, not 2. I also tried for 3^2, like this:

? multable(3,x^2+x+1,x)
0       0       0       0       0       0       0       0       0     
+  
0       7       8       6       7       8       6       7       8     
+  
0       8       6       7       8       6       7       8       6     
+  
0       6       7       8       6       7       8       6       7     
+  
0       7       8       6       7       8       6       7       8     
+  
0       8       6       7       8       6       7       8       6     
+  
0       6       7       8       6       7       8       6       7     
+  
0       7       8       6       7       8       6       7       8     
+  
0       8       6       7       8       6       7       8       6
[download]

This table doesn't look right at all. What could be going wrong?

Update:For the 3^2 case, I see that I didn't use a correct primitive polynomial for GF(3). I tried "x^2+2*x+2" and it looks a lot better. Now I just need to find a way to get other primitive polynomials...

Update2: I found a program than can compute a primitive polynomial of any order for GF(n), here.