# gfconv

Multiply polynomials over Galois field

## Syntax

## Description

returns a row vector that specifies the GF(2) polynomial coefficients in order of
ascending powers. The returned vector results from the multiplication of GF(2) polynomials
`c`

= gfconv(`a`

,`b`

) `a`

and `b`

. The polynomial degree of the
resulting GF(2) polynomial `c`

equals the degree of
`a`

plus the degree of `b`

.

For additional information, see Tips.

multiplies two GF(`c`

= gfconv(`a`

,`b`

,`field`

)*p ^{m}*)
polynomials, where

`field`

is a matrix containing the *m*-tuple of all elements in GF(

*p*).

^{m}*p*is a prime number, and m is a positive integer.

`a`

,
`b`

, and `c`

are in the same Galois field. In this syntax, each coefficient is specified in exponential format, specifically
[-Inf, 0, 1, 2, ...]. The elements in exponential format represent the
`field`

elements [0, 1, *α*,
*α*^{2}, ...] relative to some primitive
element *α* of
GF(*p ^{m}*).

returns a row vector that specifies the GF(2) polynomial coefficients in order of
ascending powers. The returned vector results from the multiplication of the GF(2)
polynomials specified in `c`

= gfconv(`polys`

) `polys`

. The polynomial degree of the
resulting GF(2) polynomial `c`

equals the sum of the degrees of the
polynomials contained in `polys`

. Use this syntax when
`polys`

specifies polynomials as a cell array of character vectors or
as a string array.

multiplies the GF(`c`

= gfconv(`polys`

,`field`

)*p ^{m}*) polynomials in

`polys`

, where `field`

is a matrix containing the
*m*-tuple of all elements in GF(

*p*).

^{m}*p*is a prime number, and

*m*is a positive integer.

`a`

,
`b`

, and `c`

are in the same Galois field.In this syntax, each coefficient is specified in exponential format, specifically
[-Inf, 0, 1, 2, ...]. The elements in exponential format represent the
`field`

elements [0, 1, *α*,
*α*^{2}, ...] relative to some primitive
element *α* of
GF(*p ^{m}*).

## Examples

## Input Arguments

## Output Arguments

## Tips

The gfconv function performs computations in GF(

*p*), where^{m}*p*is prime, and*m*is a positive integer. It multiplies polynomials over a Galois field. To work in GF(2), you can also use the^{m}`conv`

function of the`gf`

object with Galois arrays. For details, see Multiplication and Division of Polynomials.To multiply elements of a Galois field, use

`gfmul`

instead of`gfconv`

. Algebraically, multiplying polynomials over a Galois field is equivalent to convolving vectors containing the coefficients of the polynomials. This convolution operation uses arithmetic over the same Galois field.

## Version History

**Introduced before R2006a**