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That is one (non-optimal) way
sage: k = GF(2^4)
sage: R.<x> = k[]
sage: p = x^3
sage: for a in k:
....: print("".join(map(str,a)), "->", "".join(map(str,p(a))))
0000 -> 0000
0100 -> 0001
0010 -> 0011
0001 -> 0101
1100 -> 1111
0110 -> 1000
0011 -> 0001
1101 -> 0011
1010 -> 0101
0101 -> 1111
1110 -> 1000
0111 -> 0001
1111 -> 0011
1011 -> 0101
1001 -> 1111
1000 -> 1000
