1 - A Program for Computing Primitive Polynomials.
  2
  3Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
  4GNU General Public License.  This is free software, and you are welcome
  5to redistribute it under certain conditions; see the GNU General Public License
  6for details.
  7
  8
  9
 10
 11
 12Primitive polynomial modulo 2 of degree 2
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 14 x ^ 2 +  x + 1
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 17
 18 - A Program for Computing Primitive Polynomials.
 19
 20Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
 21GNU General Public License.  This is free software, and you are welcome
 22to redistribute it under certain conditions; see the GNU General Public License
 23for details.
 24
 25
 26
 27
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 29Primitive polynomial modulo 2 of degree 17
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 31 x ^ 17 +  x ^ 3 + 1
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 35 - A Program for Computing Primitive Polynomials.
 36
 37Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
 38GNU General Public License.  This is free software, and you are welcome
 39to redistribute it under certain conditions; see the GNU General Public License
 40for details.
 41
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 44
 45
 46Primitive polynomial modulo 2 of degree 43
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 48 x ^ 43 +  x ^ 6 +  x ^ 4 +  x ^ 3 + 1
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 52 - A Program for Computing Primitive Polynomials.
 53
 54Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
 55GNU General Public License.  This is free software, and you are welcome
 56to redistribute it under certain conditions; see the GNU General Public License
 57for details.
 58
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 61
 62
 63Primitive polynomial modulo 2 of degree 62
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 65 x ^ 62 +  x ^ 6 +  x ^ 5 +  x ^ 3 + 1
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 69 - A Program for Computing Primitive Polynomials.
 70
 71Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
 72GNU General Public License.  This is free software, and you are welcome
 73to redistribute it under certain conditions; see the GNU General Public License
 74for details.
 75
 76
 77
 78
 79
 80Primitive polynomial modulo 3 of degree 30
 81
 82 x ^ 30 +  x + 2
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 85
 86 - A Program for Computing Primitive Polynomials.
 87
 88Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
 89GNU General Public License.  This is free software, and you are welcome
 90to redistribute it under certain conditions; see the GNU General Public License
 91for details.
 92
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 95
 96
 97Primitive polynomial modulo 5 of degree 22
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 99 x ^ 22 +  x ^ 2 +  x + 3
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103 - A Program for Computing Primitive Polynomials.
104
105Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
106GNU General Public License.  This is free software, and you are welcome
107to redistribute it under certain conditions; see the GNU General Public License
108for details.
109
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114Primitive polynomial modulo 7 of degree 16
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116 x ^ 16 + 2 x + 3
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120 - A Program for Computing Primitive Polynomials.
121
122Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
123GNU General Public License.  This is free software, and you are welcome
124to redistribute it under certain conditions; see the GNU General Public License
125for details.
126
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131Primitive polynomial modulo 17 of degree 14
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133 x ^ 14 +  x ^ 2 + 2 x + 6
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137 - A Program for Computing Primitive Polynomials.
138
139Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
140GNU General Public License.  This is free software, and you are welcome
141to redistribute it under certain conditions; see the GNU General Public License
142for details.
143
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148Primitive polynomial modulo 137 of degree 7
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150 x ^ 7 +  x + 3
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154 - A Program for Computing Primitive Polynomials.
155
156Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
157GNU General Public License.  This is free software, and you are welcome
158to redistribute it under certain conditions; see the GNU General Public License
159for details.
160
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164
165Primitive polynomial modulo 223 of degree 8
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167 x ^ 8 +  x + 51
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171 - A Program for Computing Primitive Polynomials.
172
173Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
174GNU General Public License.  This is free software, and you are welcome
175to redistribute it under certain conditions; see the GNU General Public License
176for details.
177
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182Primitive polynomial modulo 557 of degree 6
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184 x ^ 6 +  x + 5
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188 - A Program for Computing Primitive Polynomials.
189
190Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
191GNU General Public License.  This is free software, and you are welcome
192to redistribute it under certain conditions; see the GNU General Public License
193for details.
194
195
196Factoring r = 15 into
197    3 5 
198
199Total number of primitive polynomials = 2.  Begin testing...
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205Primitive polynomial modulo 2 of degree 4
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207 x ^ 4 +  x + 1
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209
210+--------- Statistics -----------------------------------------------------------------
211|
212| Total num. degree   4 polynomials mod   2 :    16
213| Actually tested :                              4
214| Const. coeff. was primitive root :               2
215| Free of linear factors :                         1
216| Irreducible or irred. to power :                 1
217| Had order r (x^r = integer) :                    1
218| Passed const. coeff. test :                      1
219| Had order m (x^m != integer) :                   1
220|
221+--------------------------------------------------------------------------------------
222
223Confirming polynomial is primitive with an independent check.
224Warning:  You may wait an impossibly long time!
225
226    -Polynomial is confirmed to be primitive.
227
228
229 - A Program for Computing Primitive Polynomials.
230
231Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
232GNU General Public License.  This is free software, and you are welcome
233to redistribute it under certain conditions; see the GNU General Public License
234for details.
235
236
237Factoring r = 121 into
238    11^2 
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240Total number of primitive polynomials = 22.  Begin testing...
241
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245
246Primitive polynomial modulo 3 of degree 5
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248 x ^ 5 + 2 x + 1
249
250
251+--------- Statistics -----------------------------------------------------------------
252|
253| Total num. degree   5 polynomials mod   3 :    243
254| Actually tested :                              8
255| Const. coeff. was primitive root :               3
256| Free of linear factors :                         1
257| Irreducible or irred. to power :                 1
258| Had order r (x^r = integer) :                    1
259| Passed const. coeff. test :                      1
260| Had order m (x^m != integer) :                   1
261|
262+--------------------------------------------------------------------------------------
263
264Confirming polynomial is primitive with an independent check.
265Warning:  You may wait an impossibly long time!
266
267    -Polynomial is confirmed to be primitive.
268
269
270 - A Program for Computing Primitive Polynomials.
271
272Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
273GNU General Public License.  This is free software, and you are welcome
274to redistribute it under certain conditions; see the GNU General Public License
275for details.
276
277Total number of primitive polynomials = 6.  Begin testing...
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281Primitive polynomial 1 of 6 modulo 2 of degree 5
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283 x ^ 5 +  x ^ 2 + 1
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288Primitive polynomial 2 of 6 modulo 2 of degree 5
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290 x ^ 5 +  x ^ 3 + 1
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295Primitive polynomial 3 of 6 modulo 2 of degree 5
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297 x ^ 5 +  x ^ 3 +  x ^ 2 +  x + 1
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302Primitive polynomial 4 of 6 modulo 2 of degree 5
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304 x ^ 5 +  x ^ 4 +  x ^ 2 +  x + 1
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309Primitive polynomial 5 of 6 modulo 2 of degree 5
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311 x ^ 5 +  x ^ 4 +  x ^ 3 +  x + 1
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316Primitive polynomial 6 of 6 modulo 2 of degree 5
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318 x ^ 5 +  x ^ 4 +  x ^ 3 +  x ^ 2 + 1
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324 - A Program for Computing Primitive Polynomials.
325
326Primpoly comes with ABSOLUTELY NO WARRANTY; for details see the
327GNU General Public License.  This is free software, and you are welcome
328to redistribute it under certain conditions; see the GNU General Public License
329for details.
330
331ERROR:  Expecting two arguments, p and n.
332
333This program generates a primitive polynomial of degree n modulo p.
334
335Usage:    primpoly p n
336
337Example:  primpoly 2 4 
338          generates the fourth degree polynomial
339
340          x ^ 4 + x + 1, whose coefficients use modulo 2 arithmetic.
341
342Primitive polynomials find many uses in mathematics and communications 
343engineering:
344   * Generation of pseudonoise (PN) sequences for spread spectrum
345     communications and chip fault testing.
346   * Generation of CRC and Hamming codes.
347   * Generation of Galois (finite) fields for use in decoding Reed-Solomon
348     and BCH error correcting codes.
349
350Options:
351   pp -c 2 4
352       does an addtional time consuming double check on the primitivity.
353   pp -s 2 4
354       prints search statistics.
355   pp -a 2 4
356       lists ALL primitive polynomials of degree 4 modulo 2.