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The number of monic irreducible polynomials over GF(q) of given trace.

Below we use x = RootOf( z^2+z+1 ) and y = 1+x.

GF(2) GF(3) GF(4) GF(5)
(trace)
n 10 1,20 1,x,y0 1,2,3,40
1 1 1 1 1 1 1 1 1
2 1 0 1 1 2 0 2 2
3 1 1 3 2 5 5 8 8
4 2 1 6 6 16 12 30 30
5 3 3 16 16 51 51 125 124
6 5 4 39 38 170 160 516 516
7 9 9 104 104 585 585 2232 2232
8 16 14 270 270 2048 2016 9750 9750
9 28 28 729 726 7280 7280 43400 43400
10 51 48 1960 1960 26214 26112 195250 195248
11 93 93 5368 5368 95325 95325 887784 887784
12 170 165 14742 14736 349520 349180 4068740 4068740
13 315 315 40880 40880 1290555 1290555 18780048 18780048
14 585 576 113828 113828 4793490 4792320 87191964 87191964
15 1091 1091 318864 318848 17895679 17895679 406901000 406900992
16 2048 2032 896670 896670 67108864 67104768 1907343750 1907343750

Examples:

Further Notes:


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Created December 13, 1999 by Frank Ruskey.
It was last updated Wednesday, 10-May-2006 10:32:14 PDT.
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