
 - 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.


