# Documentation

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# gfconv

Multiply polynomials over Galois field

## Syntax

```c = gfconv(a,b) c = gfconv(a,b,p) c = gfconv(a,b,field) ```

## Description

### Note

This function performs computations in GF(pm), where p is prime. To work in GF(2m), use the `conv` function with Galois arrays. For details, see Multiplication and Division of Polynomials.

The `gfconv` function multiplies polynomials over a Galois field. (To multiply elements of a Galois field, use `gfmul` instead.) Algebraically, multiplying polynomials over a Galois field is equivalent to convolving vectors containing the polynomials' coefficients, where the convolution operation uses arithmetic over the same Galois field.

`c = gfconv(a,b) ` multiplies two GF(2) polynomials, `a` and `b`, which can be either polynomial character vectors or numeric vectors. The polynomial degree of the resulting GF(2) polynomial `c` equals the degree of `a` plus the degree of `b`.

`c = gfconv(a,b,p) ` multiplies two GF(`p`) polynomials, where `p` is a prime number. `a`, `b`, and `c` are row vectors that give the coefficients of the corresponding polynomials in order of ascending powers. Each coefficient is between 0 and `p`-1.

`c = gfconv(a,b,field) ` multiplies two GF(pm) polynomials, where p is a prime number and m is a positive integer. `a`, `b`, and `c` are row vectors that list the exponential formats of the coefficients of the corresponding polynomials, in order of ascending powers. The exponential format is relative to some primitive element of GF(pm). `field` is the matrix listing all elements of GF(pm), arranged relative to the same primitive element. See Representing Elements of Galois Fields for an explanation of these formats.

## Examples

collapse all

Multiply and over GF(3).

`gfc = gfconv([1 1 0 0 1],[0 1 1],3)`
```gfc = 0 1 2 1 0 1 1 ```

The result corresponds to .

## See Also

#### Introduced before R2006a

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