# gfprimdf

Provide default primitive polynomials for Galois field

## Syntax

```pol = gfprimdf(m) pol = gfprimdf(m,p) ```

## Description

Note

This function performs computations in GF(pm), where p is prime. To work in GF(2m), use the `primpoly` function. For details, see Finding Primitive Polynomials in Primitive Polynomials and Element Representations.

`pol = gfprimdf(m)` outputs the default primitive polynomial `pol` in GF(2m).

`pol = gfprimdf(m,p)` returns the row vector that gives the coefficients, in order of ascending powers, of the default primitive polynomial for GF(pm). `m` is a positive integer and `p` is a prime number.

## Examples

collapse all

Find the default primitive polynomial for GF(52) by using the `gfprimdf` function. Then use the `gfpretty` function to display it in polynomial format.

`pol = gfprimdf(2,5)`
```pol = 1×3 2 1 1 ```
`gfpretty(pol)`
``` 2 2 + X + X ```

Find the default primitive polynomials for a range of Galois fields by using the `gfprimdf` function.

Use the `gfpretty` function to display the default primitive polynomial for each of the fields GF(3m), where the range for m is [3, 5].

```for m = 3:5 gfpretty(gfprimdf(m,3)) end```
``` 3 1 + 2 X + X 4 2 + X + X 5 1 + 2 X + X ```