# gfadd

Add polynomials over Galois field

## Syntax

`c = gfadd(a,b) `

c = gfadd(a,b,p)

c = gfadd(a,b,p,len)

c = gfadd(a,b,field)

## Description

**Note**

This function performs computations in GF(p^{m})
where p is prime. To work in GF(2^{m}), apply
the + operator to Galois arrays of equal size. For details, see Example: Addition and Subtraction.

`c = gfadd(a,b) `

adds
two GF(2) polynomials, `a`

and `b`

,
which can be either polynomial character vectors or
numeric vectors. If `a`

and `b`

are
vectors of the same orientation but different lengths, then the shorter
vector is zero-padded. If `a`

and `b`

are
matrices they must be of the same size.

`c = gfadd(a,b,p) `

adds
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.
If `a`

and `b`

are matrices of the
same size, the function treats each row independently.

`c = gfadd(a,b,p,len) `

adds
row vectors `a`

and `b`

as in the
previous syntax, except that it returns a row vector of length `len`

.
The output `c`

is a truncated or extended representation
of the sum. If the row vector corresponding to the sum has fewer than `len`

entries
(including zeros), extra zeros are added at the end; if it has more
than `len`

entries, entries from the end are removed.

`c = gfadd(a,b,field) `

adds
two GF(p^{m}) elements, where m is a positive
integer. `a`

and `b`

are the exponential
format of the two elements, relative to some primitive element of
GF(p^{m}). `field`

is the
matrix listing all elements of GF(p^{m}),
arranged relative to the same primitive element. `c`

is
the exponential format of the sum, relative to the same primitive
element. See Representing Elements of Galois Fields for an explanation
of these formats. If `a`

and `b`

are
matrices of the same size, the function treats each element independently.

## Examples

## Version History

**Introduced before R2006a**