Below a table of binary irreducible non-primitive polynomials are given which have polynomials w(x) of weight two and of lowest possible degree. Listed are only degrees m less or equal 400 for which no primitive polynomials exist which have weight two w(x) of lowest degree. For the polynomial w(x) the equation w(x)2 = x mod q(x) holds. The irreducible polynomials of the table are given in hexadecimal form.
| m | q(x) | w(x) |
| 28 | 0x10000003 | x 14 + 1 |
| 30 | 0x40000003 | x 15 + 1 |
| 46 | 0x400000000003 | x 23 + 1 |
| 147 | 0x8000000000000000000000002000000000001 | x 74 + x 25 |
| 155 | 0x800000000000000200000000000000000000001 | x 78 + x 47 |
| 172 | 0x10000000000000000000000000000000000000000003 | x 86 + 1 |
| 253 | 0x2000000000008000000000000000000000000000000000000000000000000001 | x 127 + x 104 |
| 303 | 0x8000000000000000000000000000000000000000000000000000000000000000000000000003 | x 152 + x |
| 321 | 0x200000000000000000000000000000000000000000000000000000000000000000000020000000001 | x 161 + x 21 |
| 351 | 0x8000000000000000000000000000000000000000000000000000000000000000000080000000000000000001 | x 176 + x 40 |
| 385 | 0x2000000000000000000000000000000000000000000000000000000000000000000008000000000000000000000000001 | x 193 + x 56 |
| 399 | 0x8000000000000000000000000000000000000000000000000000000000000000000000000000000000000002000000000001 | x 200 + x 25 |