# # Complete list of binary irreducible normal polynomials # whose roots are a self-dual basis, up to degree 19. # There are no such polynomials with degree a multiple of 4. # Primitive polynomials are marked by a P. #. # Generated by Joerg Arndt, 2009-January-27 # ## n=2 #S = 1 #SP = 1 2,1,0 P ## n=3 #S = 1 #SP = 1 3,2,0 P ## n=4 #S = 0 #SP = 0 ## n=5 #S = 1 #SP = 1 5,4,2,1,0 P ## n=6 #S = 2 #SP = 1 6,5,4,2,0 6,5,4,1,0 P ## n=7 #S = 1 #SP = 1 7,6,4,1,0 P ## n=8 #S = 0 #SP = 0 ## n=9 #S = 3 #SP = 2 9,8,6,5,4,1,0 P 9,8,6,3,0 9,8,6,3,2,1,0 P ## n=10 #S = 4 #SP = 3 10,9,8,6,3,2,0 P 10,9,8,5,4,3,0 P 10,9,8,5,3,1,0 10,9,8,6,4,3,0 P ## n=11 #S = 3 #SP = 3 11,10,8,7,6,5,0 P 11,10,8,5,2,1,0 P 11,10,8,4,3,2,0 P ## n=12 #S = 0 #SP = 0 ## n=13 #S = 5 #SP = 5 13,12,10,6,0 P 13,12,10,7,4,3,0 P 13,12,10,9,8,3,2,1,0 P 13,12,10,9,8,6,4,1,0 P 13,12,10,9,8,7,6,4,3,2,0 P ## n=14 #S = 8 #SP = 4 14,13,12,10,6,3,2,1,0 P 14,13,12,9,7,5,3,2,0 14,13,12,9,8,6,5,2,0 14,13,12,10,8,6,5,4,2,1,0 P 14,13,12,9,5,3,2,1,0 14,13,12,10,7,5,4,1,0 P 14,13,12,10,8,4,2,1,0 14,13,12,9,8,1,0 P ## n=15 #S = 15 #SP = 11 15,14,12,11,10,5,3,1,0 P 15,14,12,8,5,3,0 15,14,12,7,5,1,0 P 15,14,12,6,5,4,2,1,0 P 15,14,12,11,10,7,6,4,2,1,0 P 15,14,12,9,8,7,6,5,3,2,0 15,14,12,11,10,7,6,4,0 P 15,14,12,9,7,3,2,1,0 P 15,14,12,11,10,8,7,5,3,2,0 P 15,14,12,9,7,5,4,2,0 15,14,12,9,8,7,6,4,0 P 15,14,12,9,6,5,3,1,0 P 15,14,12,11,10,4,0 15,14,12,9,7,5,0 P 15,14,12,8,7,6,5,4,3,2,0 P ## n=16 #S = 0 #SP = 0 ## n=17 #S = 17 #SP = 17 17,16,14,13,12,11,10,9,7,5,3,1,0 P 17,16,14,13,12,11,10,8,6,3,2,1,0 P 17,16,14,13,12,11,10,8,5,1,0 P 17,16,14,9,7,5,4,2,0 P 17,16,14,11,10,9,8,7,3,1,0 P 17,16,14,9,7,6,4,1,0 P 17,16,14,11,8,4,0 P 17,16,14,13,12,5,4,3,2,1,0 P 17,16,14,10,9,8,7,6,3,1,0 P 17,16,14,10,9,8,4,3,2,1,0 P 17,16,14,13,12,10,9,6,4,1,0 P 17,16,14,10,9,8,5,2,0 P 17,16,14,13,12,11,9,8,7,6,5,4,3,2,0 P 17,16,14,9,6,5,4,3,0 P 17,16,14,13,12,10,9,7,6,3,0 P 17,16,14,11,10,9,8,6,4,1,0 P 17,16,14,11,10,7,6,5,4,2,0 P ## n=18 #S = 48 #SP = 25 18,17,16,14,10,7,5,4,0 18,17,16,13,12,11,10,9,5,4,2,1,0 18,17,16,14,9,7,6,4,0 P 18,17,16,14,12,11,10,9,6,5,3,2,0 P 18,17,16,13,10,7,6,4,3,2,0 P 18,17,16,13,11,10,7,5,0 18,17,16,14,12,11,10,9,7,5,2,1,0 P 18,17,16,13,12,11,10,9,6,5,4,2,0 18,17,16,14,12,6,4,1,0 P 18,17,16,14,11,10,7,4,3,2,0 P 18,17,16,13,12,11,7,6,5,4,0 18,17,16,13,11,10,6,1,0 P 18,17,16,14,10,2,0 18,17,16,14,11,9,8,6,5,2,0 18,17,16,13,11,9,8,3,0 18,17,16,14,12,11,10,9,8,7,5,4,3,2,0 18,17,16,14,12,10,9,8,7,6,5,4,3,2,0 P 18,17,16,14,10,7,6,1,0 18,17,16,13,12,10,9,8,2,1,0 18,17,16,14,12,7,3,1,0 P 18,17,16,14,9,7,4,3,2,1,0 18,17,16,14,10,7,5,1,0 P 18,17,16,14,11,9,4,3,0 P 18,17,16,14,9,8,7,6,2,1,0 P 18,17,16,14,10,6,3,1,0 P 18,17,16,13,11,10,8,7,5,1,0 P 18,17,16,14,12,7,6,5,4,3,2,1,0 P 18,17,16,13,12,10,9,8,7,6,4,3,0 P 18,17,16,13,12,11,8,7,5,4,0 18,17,16,14,12,8,7,6,5,3,0 18,17,16,13,11,10,8,7,4,2,0 18,17,16,13,12,11,7,6,4,2,0 18,17,16,13,12,10,9,7,0 P 18,17,16,14,11,10,8,5,2,1,0 18,17,16,14,11,10,8,7,0 P 18,17,16,13,10,8,5,2,0 18,17,16,14,12,11,5,4,3,2,0 P 18,17,16,14,12,10,9,7,5,4,2,1,0 P 18,17,16,14,12,11,8,6,0 18,17,16,13,10,8,7,4,2,1,0 18,17,16,13,11,10,7,6,5,4,2,1,0 18,17,16,14,12,7,4,3,0 18,17,16,13,12,11,8,7,6,5,4,1,0 P 18,17,16,13,11,9,8,6,4,3,2,1,0 P 18,17,16,14,12,10,9,7,6,5,3,1,0 18,17,16,14,12,3,2,1,0 P 18,17,16,13,12,11,8,6,5,3,0 P 18,17,16,14,10,8,7,6,4,2,0 P ## n=19 #S = 27 #SP = 27 19,18,16,15,14,13,12,10,9,8,5,3,2,1,0 P 19,18,16,12,7,3,0 P 19,18,16,11,8,6,4,1,0 P 19,18,16,15,14,12,10,7,5,1,0 P 19,18,16,13,12,11,10,9,6,3,0 P 19,18,16,15,14,11,10,7,6,2,0 P 19,18,16,10,6,4,3,1,0 P 19,18,16,13,12,5,4,2,0 P 19,18,16,15,14,11,10,8,7,4,2,1,0 P 19,18,16,12,11,10,9,3,2,1,0 P 19,18,16,12,9,8,7,6,5,3,2,1,0 P 19,18,16,15,14,12,10,9,8,7,6,4,3,1,0 P 19,18,16,15,14,12,11,7,5,1,0 P 19,18,16,13,12,7,6,5,4,3,2,1,0 P 19,18,16,13,12,11,10,9,6,4,3,2,0 P 19,18,16,15,14,13,4,3,0 P 19,18,16,15,14,13,11,10,9,6,4,1,0 P 19,18,16,15,14,8,7,5,3,2,0 P 19,18,16,15,14,11,10,6,5,3,2,1,0 P 19,18,16,13,11,7,5,4,3,1,0 P 19,18,16,15,14,11,10,9,8,6,2,1,0 P 19,18,16,15,14,13,12,11,5,4,2,1,0 P 19,18,16,13,10,7,0 P 19,18,16,15,14,3,2,1,0 P 19,18,16,12,11,10,6,5,3,1,0 P 19,18,16,13,11,1,0 P 19,18,16,13,10,6,4,1,0 P ## n=20 #S = 0 #SP = 0