EE4253 Digital Communications Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada

Prime Polynomials (2..511)

Binary values expressed as polynomials can readily be manipulated using the rules of binary arithmetic.

The table below shows all prime polynomials from 2..511 (these are unrelated to prime decimals!). Try the LRS link to see the corresponding Linear Recursive Sequence.

Polynomials leading to maximum length sequences are shown highlighted (*) and are called primitive polynomials.

 With the MATLAB Communications Toolbox the primitive polynomials of order N may be found using primpoly( N, 'all'). For example: ```>> primpoly ( 6, 'all' ) ans = 67 91 97 103 109 115 ``` Which is a list (in decimal) of all the primitive polynomials of order 6 identified in the table below.

For larger numbers, try the Online Factoring Tool

 DECIMAL BINARY POLYNOMIAL PRIME FACTORS 2 10 x prime [ LRS ] 3 11 x+1 prime [ LRS ] * 7 111 x2+x+1 prime [ LRS ] * 11 1011 x3+x+1 prime [ LRS ] * 13 1101 x3+x2+1 prime [ LRS ] * 19 10011 x4+x+1 prime [ LRS ] * 25 11001 x4+x3+1 prime [ LRS ] * 31 11111 x4+x3+x2+x+1 prime [ LRS ] 37 100101 x5+x2+1 prime [ LRS ] * 41 101001 x5+x3+1 prime [ LRS ] * 47 101111 x5+x3+x2+x+1 prime [ LRS ] * 55 110111 x5+x4+x2+x+1 prime [ LRS ] * 59 111011 x5+x4+x3+x+1 prime [ LRS ] * 61 111101 x5+x4+x3+x2+1 prime [ LRS ] * 67 1000011 x6+x+1 prime [ LRS ] * 73 1001001 x6+x3+1 prime [ LRS ] 87 1010111 x6+x4+x2+x+1 prime [ LRS ] 91 1011011 x6+x4+x3+x+1 prime [ LRS ] * 97 1100001 x6+x5+1 prime [ LRS ] * 103 1100111 x6+x5+x2+x+1 prime [ LRS ] * 109 1101101 x6+x5+x3+x2+1 prime [ LRS ] * 115 1110011 x6+x5+x4+x+1 prime [ LRS ] * 117 1110101 x6+x5+x4+x2+1 prime [ LRS ] 131 10000011 x7+x+1 prime [ LRS ] * 137 10001001 x7+x3+1 prime [ LRS ] * 143 10001111 x7+x3+x2+x+1 prime [ LRS ] * 145 10010001 x7+x4+1 prime [ LRS ] * 157 10011101 x7+x4+x3+x2+1 prime [ LRS ] * 167 10100111 x7+x5+x2+x+1 prime [ LRS ] * 171 10101011 x7+x5+x3+x+1 prime [ LRS ] * 185 10111001 x7+x5+x4+x3+1 prime [ LRS ] * 191 10111111 x7+x5+x4+x3+x2+x+1 prime [ LRS ] * 193 11000001 x7+x6+1 prime [ LRS ] * 203 11001011 x7+x6+x3+x+1 prime [ LRS ] * 211 11010011 x7+x6+x4+x+1 prime [ LRS ] * 213 11010101 x7+x6+x4+x2+1 prime [ LRS ] * 229 11100101 x7+x6+x5+x2+1 prime [ LRS ] * 239 11101111 x7+x6+x5+x3+x2+x+1 prime [ LRS ] * 241 11110001 x7+x6+x5+x4+1 prime [ LRS ] * 247 11110111 x7+x6+x5+x4+x2+x+1 prime [ LRS ] * 253 11111101 x7+x6+x5+x4+x3+x2+1 prime [ LRS ] * 283 100011011 x8+x4+x3+x+1 prime [ LRS ] 285 100011101 x8+x4+x3+x2+1 prime [ LRS ] * 299 100101011 x8+x5+x3+x+1 prime [ LRS ] * 301 100101101 x8+x5+x3+x2+1 prime [ LRS ] * 313 100111001 x8+x5+x4+x3+1 prime [ LRS ] 319 100111111 x8+x5+x4+x3+x2+x+1 prime [ LRS ] 333 101001101 x8+x6+x3+x2+1 prime [ LRS ] * 351 101011111 x8+x6+x4+x3+x2+x+1 prime [ LRS ] * 355 101100011 x8+x6+x5+x+1 prime [ LRS ] * 357 101100101 x8+x6+x5+x2+1 prime [ LRS ] * 361 101101001 x8+x6+x5+x3+1 prime [ LRS ] * 369 101110001 x8+x6+x5+x4+1 prime [ LRS ] * 375 101110111 x8+x6+x5+x4+x2+x+1 prime [ LRS ] 379 101111011 x8+x6+x5+x4+x3+x+1 prime [ LRS ] 391 110000111 x8+x7+x2+x+1 prime [ LRS ] * 395 110001011 x8+x7+x3+x+1 prime [ LRS ] 397 110001101 x8+x7+x3+x2+1 prime [ LRS ] * 415 110011111 x8+x7+x4+x3+x2+x+1 prime [ LRS ] 419 110100011 x8+x7+x5+x+1 prime [ LRS ] 425 110101001 x8+x7+x5+x3+1 prime [ LRS ] * 433 110110001 x8+x7+x5+x4+1 prime [ LRS ] 445 110111101 x8+x7+x5+x4+x3+x2+1 prime [ LRS ] 451 111000011 x8+x7+x6+x+1 prime [ LRS ] * 463 111001111 x8+x7+x6+x3+x2+x+1 prime [ LRS ] * 471 111010111 x8+x7+x6+x4+x2+x+1 prime [ LRS ] 477 111011101 x8+x7+x6+x4+x3+x2+1 prime [ LRS ] 487 111100111 x8+x7+x6+x5+x2+x+1 prime [ LRS ] * 499 111110011 x8+x7+x6+x5+x4+x+1 prime [ LRS ] 501 111110101 x8+x7+x6+x5+x4+x2+1 prime [ LRS ] * 505 111111001 x8+x7+x6+x5+x4+x3+1 prime [ LRS ]

 Tue May 21 13:13:26 ADT 2013 Last Updated: 17 NOV 2003 Richard Tervo [ tervo@unb.ca ] Back to the course homepage...