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.
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11
12Primitive polynomial modulo 2 of degree 2
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14 x ^ 2 + x + 1
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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.
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28
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.
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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.
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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.
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80Primitive polynomial modulo 3 of degree 30
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82 x ^ 30 + x + 2
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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.
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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.
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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.
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130
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.
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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.
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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.
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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
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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.
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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...
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245
246Primitive polynomial modulo 3 of degree 5
247
248 x ^ 5 + 2 x + 1
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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.
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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
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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.