This table is from: /* Error Correction Coding: Mathematical Methods and Algorithms by Todd K. Moon, Utah State University published by Wiley, 2005 756+xliii pages, plus Web page. (ISBN 0-471-64800-0) */ 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