Default primitive polynomials
The table below lists the default primitive polynomials of degree $k$ over $\mathbb{F}_2$ for $k \in [1 : 24]$. The polynomial $p(X)$ is represented as a binary number, where the leftmost bit stands for the highest degree term. For example, the polynomial $p(X) = X^3 + X + 1$ is represented as 0b1011.
Source: LC04, Table 2.7, p.42.
| Degree $k$ | Primitive polynomial $p(X)$ | Degree $k$ | Primitive polynomial $p(X)$ |
|---|---|---|---|
| $1$ | 0b11 |
$13$ | 0b10000000011011 |
| $2$ | 0b111 |
$14$ | 0b100010001000011 |
| $3$ | 0b1011 |
$15$ | 0b1000000000000011 |
| $4$ | 0b10011 |
$16$ | 0b11010000000010001 |
| $5$ | 0b100101 |
$17$ | 0b100000000000001001 |
| $6$ | 0b1000011 |
$18$ | 0b1000000000010000001 |
| $7$ | 0b10001001 |
$19$ | 0b10000000000000100111 |
| $8$ | 0b100011101 |
$20$ | 0b100000000000000001001 |
| $9$ | 0b1000010001 |
$21$ | 0b1000000000000000000101 |
| $10$ | 0b10000001001 |
$22$ | 0b10000000000000000000011 |
| $11$ | 0b100000000101 |
$23$ | 0b100000000000000000100001 |
| $12$ | 0b1000001010011 |
$24$ | 0b1000000000000000010000111 |