- A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 2 of degree 2 x ^ 2 + x + 1 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 2 of degree 17 x ^ 17 + x ^ 3 + 1 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 2 of degree 43 x ^ 43 + x ^ 6 + x ^ 4 + x ^ 3 + 1 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 2 of degree 62 x ^ 62 + x ^ 6 + x ^ 5 + x ^ 3 + 1 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 3 of degree 30 x ^ 30 + x + 2 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 5 of degree 22 x ^ 22 + x ^ 2 + x + 3 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 7 of degree 16 x ^ 16 + 2 x + 3 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 17 of degree 14 x ^ 14 + x ^ 2 + 2 x + 6 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 137 of degree 7 x ^ 7 + x + 3 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 223 of degree 8 x ^ 8 + x + 51 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Primitive polynomial modulo 557 of degree 6 x ^ 6 + x + 5 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Factoring r = 15 into 3 5 Total number of primitive polynomials = 2. Begin testing... Primitive polynomial modulo 2 of degree 4 x ^ 4 + x + 1 +--------- Statistics ----------------------------------------------------------------- | | Total num. degree 4 polynomials mod 2 : 16 | Actually tested : 4 | Const. coeff. was primitive root : 2 | Free of linear factors : 1 | Irreducible or irred. to power : 1 | Had order r (x^r = integer) : 1 | Passed const. coeff. test : 1 | Had order m (x^m != integer) : 1 | +-------------------------------------------------------------------------------------- Confirming polynomial is primitive with an independent check. Warning: You may wait an impossibly long time! -Polynomial is confirmed to be primitive. - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Factoring r = 121 into 11^2 Total number of primitive polynomials = 22. Begin testing... Primitive polynomial modulo 3 of degree 5 x ^ 5 + 2 x + 1 +--------- Statistics ----------------------------------------------------------------- | | Total num. degree 5 polynomials mod 3 : 243 | Actually tested : 8 | Const. coeff. was primitive root : 3 | Free of linear factors : 1 | Irreducible or irred. to power : 1 | Had order r (x^r = integer) : 1 | Passed const. coeff. test : 1 | Had order m (x^m != integer) : 1 | +-------------------------------------------------------------------------------------- Confirming polynomial is primitive with an independent check. Warning: You may wait an impossibly long time! -Polynomial is confirmed to be primitive. - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. Total number of primitive polynomials = 6. Begin testing... Primitive polynomial 1 of 6 modulo 2 of degree 5 x ^ 5 + x ^ 2 + 1 Primitive polynomial 2 of 6 modulo 2 of degree 5 x ^ 5 + x ^ 3 + 1 Primitive polynomial 3 of 6 modulo 2 of degree 5 x ^ 5 + x ^ 3 + x ^ 2 + x + 1 Primitive polynomial 4 of 6 modulo 2 of degree 5 x ^ 5 + x ^ 4 + x ^ 2 + x + 1 Primitive polynomial 5 of 6 modulo 2 of degree 5 x ^ 5 + x ^ 4 + x ^ 3 + x + 1 Primitive polynomial 6 of 6 modulo 2 of degree 5 x ^ 5 + x ^ 4 + x ^ 3 + x ^ 2 + 1 - A Program for Computing Primitive Polynomials. Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the GNU General Public License. This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details. ERROR: Expecting two arguments, p and n. This program generates a primitive polynomial of degree n modulo p. Usage: primpoly p n Example: primpoly 2 4 generates the fourth degree polynomial x ^ 4 + x + 1, whose coefficients use modulo 2 arithmetic. Primitive polynomials find many uses in mathematics and communications engineering: * Generation of pseudonoise (PN) sequences for spread spectrum communications and chip fault testing. * Generation of CRC and Hamming codes. * Generation of Galois (finite) fields for use in decoding Reed-Solomon and BCH error correcting codes. Options: pp -c 2 4 does an addtional time consuming double check on the primitivity. pp -s 2 4 prints search statistics. pp -a 2 4 lists ALL primitive polynomials of degree 4 modulo 2.