Documentation

# 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

The command below shows that 2 + x + x2 is the default primitive polynomial for GF(52).

```pol = gfprimdf(2,5) pol = 2 1 1 ```

The code below displays the default primitive polynomial for each of the fields GF(3m), where m ranges between 3 and 5.

```for m = 3:5 gfpretty(gfprimdf(m,3)) end```

The output is below.

``` 3 1 + 2 X + X 4 2 + X + X 5 1 + 2 X + X ```