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minpol

Find minimal polynomial of Galois field element

Syntax

```pl = minpol(x) ```

Description

`pl = minpol(x)` finds the minimal polynomial of each element in the Galois column vector, `x`. The output `pl` is an array in GF(2). The kth row of `pl` lists the coefficients, in order of descending powers, of the minimal polynomial of the kth element of `x`.

Note

The output is in GF(2) even if the input is in a different Galois field.

Examples

The code below uses `m = 4` and finds that the minimal polynomial of `gf(2,m)` is just the primitive polynomial used for the field GF(`2^m`). This is true for any value of `m`, not just the value used in the example.

```m = 4; A = gf(2,m) pl = minpol(A)```

The output is below. Notice that the row vector `[1 0 0 1 1]` represents the polynomial `D^4 + D + 1`.

```A = GF(2^4) array. Primitive polynomial = D^4+D+1 (19 decimal) Array elements = 2 pl = GF(2) array. Array elements = 1 0 0 1 1 ```

Another example is in Minimal Polynomials.