/* The following functions generate lists of CCZ-inequivalent representatives from all currently known infinite families over GF(2^n) with n in the range from 6 to 11. */ function listAPNRepresentatives6() n := 6; FF

:= GF(2^n); P := PolynomialRing(FF); G6 := [ x^3, x^6 + x^9 + p^7*x^48, p*x^3 + p^4*x^24 + x^17 ]; return G6; end function; function listAPNRepresentatives7() n := 7; FF

:= GF(2^n); P := PolynomialRing(FF); G7 := [ x^3, x^5, x^9, x^13, x^57, x^63, x^3 + Trace(x^9) ]; return G7; end function; function listAPNRepresentatives8() n := 8; FF

:= GF(2^n); P := PolynomialRing(FF); G8 := [ x^3, x^9, x^57, x^3 + x^17 + p^48*x^18 + p^3*x^33 + p*x^34 + x^48, x^3 + Trace(x^9), x^3 + p^(-1)*Trace(p^3*x^9), (x + x^16)^3 + p^17*(p*x + p^16*x^16)^12 + p*(x + x^16)*(p*x + p^16*x^16) ]; return G8; end function; function listAPNRepresentatives9() n := 9; FF

:= GF(2^n); P := PolynomialRing(FF); Q := quo< P | ideal < P | x^(2^n) + x > >; Trace39 := x + x^8 + x^64; G9 := [ x^3, x^5, x^17, x^13, x^241, x^19, x^255, x^3 + Trace(x^9), P ! ( Q ! (x^3 + Evaluate(Trace39, x^9 + x^18)) ), P ! ( Q ! (x^3 + Evaluate(Trace39,x^18 + x^36)) ), p^337*x^129 + p^424*x^66 + p^2*x^17 + p*x^10 + p^34*x^3 ]; return G9; end function; function listAPNRepresentatives10() n := 10; FF

:= GF(2^n); P := PolynomialRing(FF); G10 := [ x^3, x^9, x^57, x^339, x^6 + x^33 + p^31*x^192, x^72 + x^33 + p^31*x^258, x^3 + Trace(x^9), x^3 + p^(-1)*Trace(p^3*x^9), x^3 + p^341 * x^9 + p^682 * x^96 + x^288, x^3 + p^341 * x^129 + p^682 * x^96 + x^36 ]; return G10; end function; function listAPNRepresentatives11() n := 11; FF

:= GF(2^n); P := PolynomialRing(FF); G11 := [ x^3, x^5, x^9, x^17, x^33, x^13, x^57, x^241, x^993, x^35, x^287, x^1023, x^3 + Trace(x^9) ]; return G11; end function;