// output of ./demo/gf2n/all-normalpoly-demo.cc: // Description: //% Find all normal binary polynomials of degree n. //% Print all corresponding multiplier matrices. //% Cf. OEIS sequences A027362, A107222, and A272033. arg 1: 9 == n [Degree of the polynomials] default=9 arg 2: 3 == pp [How to print polynomials: 1==>binary, 2==>as poly., 3==> both, 0==>just count] default=3 arg 3: 0 == mq [Whether to print multiplication matrix] default=0 1: c = 11..11...1 P == x^9 + x^8 + x^5 + x^4 + 1 2: c = 11...1..11 P == x^9 + x^8 + x^4 + x + 1 3: c = 11111...11 P == x^9 + x^8 + x^7 + x^6 + x^5 + x + 1 4: c = 11.11.1.11 P == x^9 + x^8 + x^6 + x^5 + x^3 + x + 1 5: c = 111....1.1 P == x^9 + x^8 + x^7 + x^2 + 1 6: c = 111...1111 P == x^9 + x^8 + x^7 + x^3 + x^2 + x + 1 7: c = 11.......1 == x^9 + x^8 + 1 8: c = 11.111..11 P == x^9 + x^8 + x^6 + x^5 + x^4 + x + 1 9: c = 1111.1.1.1 P == x^9 + x^8 + x^7 + x^6 + x^4 + x^2 + 1 10: c = 1111..1.11 P == x^9 + x^8 + x^7 + x^6 + x^3 + x + 1 11: c = 11.1.11.11 P == x^9 + x^8 + x^6 + x^4 + x^3 + x + 1 12: c = 11.1..1..1 == x^9 + x^8 + x^6 + x^3 + 1 13: c = 1111111.11 P == x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x + 1 14: c = 1111...111 P == x^9 + x^8 + x^7 + x^6 + x^2 + x + 1 15: c = 11...1.1.1 P == x^9 + x^8 + x^4 + x^2 + 1 16: c = 11.1..1111 P == x^9 + x^8 + x^6 + x^3 + x^2 + x + 1 17: c = 11...11111 P == x^9 + x^8 + x^4 + x^3 + x^2 + x + 1 18: c = 111.111..1 P == x^9 + x^8 + x^7 + x^5 + x^4 + x^3 + 1 19: c = 1111.11..1 P == x^9 + x^8 + x^7 + x^6 + x^4 + x^3 + 1 20: c = 11..111.11 P == x^9 + x^8 + x^5 + x^4 + x^3 + x + 1 21: c = 11.11.11.1 P == x^9 + x^8 + x^6 + x^5 + x^3 + x^2 + 1 n=9 #= 21 #primitive = 19 #non-primitive = 2