primitive.txt

压缩文件中是Error Correction Coding - Mathematical Methods and Algorithms(Wiley 2005)作者:(Todd K. Moon )的配

Table of Primitive Polynomials


Several different polynomials are represented for most degrees.  For
example, there are fourteen different primitive polynomials listed of
degree 9.  (This is not necessarily an exhaustive list of all
polynomials for each degree.)

The numbers in the table below represent primitive polynomials.
The numbers are in octal, 

     0=000, 1=001, 2=010, 3=011
     4=100  5=101  6=110  7=111

Each octal digit in the number is replaced by its binary equivalent.
The resulting binary sequence represents the coefficients of the
primitive polynomial.  The coefficient g_0 is on the left; the
coefficient g_r is on the right. 

For example, for degree 9, the number 1021 has the expansion 
001 000 010 001,
representing the polynomial 1 + x^5 + x^9.

Note that if a polynomial is primitive, then so is its reciprocal.
For example, for the same table entry reading right-to-left, 
1 + x^4 + x^9 is also primitive.

Numbers in the table indicated with * are trinomials (have only 2
feedback connections), and  are better suited for some high-speed
applications.

This table is obtained from "Digital Communications and Spread
Spectrum Systems" by Rodger E. Ziemer and Roger L. Peterson (MacMillan
Publishing, 1985), which derives it from:

"Error Correction Codes" by W.W. Peterson and E.J. Weldon (MIT Press,
1972) 

"An Ordered Table of Primitive Polynomials over GF(2) of degrees 2
through 19 for use with Linear Maximal Sequence Generators," TM107,
Cooley Laboratory, University of Michigan, Ann Arbor, July 1972

"Coherent Spread Spectrum Systems" by J.K. Holmes (Wiley-Interscience,
1982).

Peterson and Weldon is a rich source of information about primitive
polynomials.


Information is provided in a textual format here, to make it easier to
incorporate into programs.


Degree   Octal Representation
2        7*

3        13*

4        23*

5        45*,  75,  67

6        103*,  147,  155

7        211,  217,  235,  367,  277,  325,  203*,  313,  345

8        435,  551,  747,  453,  545,  537,  703,  543

9        1021*,  1131,  1461,  1423,  1055,  1167,  1541,  
         1333,  1605,  1751,  1743,  1617,  1553,  1157

10       2011*,  2415,  3771,  2157,  3515,  2773,  2033,  
         2443,  2461,  3023,  3543,  2745,  2431,  3177

11       4005*,  4445,  4215,  4055,  6015,  7413,  4143,  
         4563,  4053,  5023,  5623,  4577,  6233,  6673

12       10123,  15647,  16533,  16047,  11015,  14127,  
          17673,  13565,  15341,  15053,  15621,  15321,  
         11417,  13505

13       20033,  23261,  24623,  23517,  30741,  21643,  
         30171,  21277,  27777,  35051,  34723,  34047,  
         32535,  31425

14       42103,  43333,  51761,  40503,  77141,  62677,  
         44103,  45145,  76303,  64457,  57231,  64167,  
         60153,  55753

15       100003*,  102043,  110013,  102067,  104307,  100317,  
         177775,  103451,  110075,  102061,  114725,  103251,  
         100021*,  100201*

16       210013,  234313,  233303,  307107,  307527,  306357,  
         201735,  272201,  242413,  270155,  302157,  210205,  
         305667,  236107

17       400011*,  400017,  400431,  525251,  410117,  400731
         411335,  444257,  600013,  403555,  525327,  411077,  
         400041*,  400101*

18       1000201*,  1000247,  1002241,  1002441,  1100045,  
         1000407,  1003011,  1020121,  1101005,  1000077,  
         1001361,  1001567,  1001727,  1002777

19       2000047,  2000641,  2001441,  2000107,  2000077,  
         2000157,  2000175,  2000257,  2000677,  2000737,  
         2001557,  2001637,  2005775,  2006677

20       4000011*,  4001051,  4004515,  6000031,  4442235

21       10000005*,  10040205,  10020045,  10040315,  10000635,  
         10103075,  10050335,  10002135,  17000075

22       20000003*,  20001043,  2222223,  25200127,  20401207,  
         20430607,  20070217

23       40000041*,  40404041,  40000063,  40010061,  50000241,  
         40220151,  40006341,  40405463,  40103271,  41224445,  
         4043561

24       100000207,  125245661,  113763063

25       200000011*,  200000017,  204000051,  200010031,  
         200402017,  252001251,  201014171,  204204057,  
         200005535,  200014731

26       400000107,  430216473,  402365755,  426225667,  
         510664323,  473167545,  411335571

27       1000000047,  1001007071,  1020024171,  1102210617,  
         1250025757,  1257242631,  1020560103,  1112225171,  
         1035530241

28       2000000011*,  2104210431,  2000025051,  2020006031,  
         2002502115,  2001601071

29       4000000005*,  4004004005,  4000010205,  4010000045,  
         4400000045,  4002200115,  4001040115,  4004204435,  
         4100060435,  4040003075,  40040642751

30       10040000007,  10104264207,  10115131333,  11362212703,  
         10343244533

31       20000000011*,  20000000017,  20000020411,  21042104211,  
         20010010017,  20005000251,  20004100071,  20202040217,  
         20000200435,  20060140231,  21042107357

32       40020000007,  40460216667,  40035532523,  42003247143,  
         41760427607

33       100000020001*,  100020024001,  104000420001,  
         100020224401,  111100021111,  100000031463,  
         104020466001,  100502430041,  100601431001

34       201000000007,  201472024107,  377000007527,  
         225213433257,  227712240037,  251132516577,  
         211636220473,  200000140003

35       400000000005*

36       1000000004001*

37       2000000012005

38       4000000000143

39       10000000000021*

40       20000012000005

61       200000000000000000047

89       400000000000000000000000000151