## Description

Note

This function performs computations in GF(pm) where p is prime. To work in GF(2m), 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(pm) 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(pm). field is the matrix listing all elements of GF(pm), 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

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Sum $2+3x+{x}^{2}$ and $4+2x+3{x}^{2}$ over GF(5).

x = gfadd([2 3 1],[4 2 3],5)
x = 1×3

1     0     4

Add the two polynomials and display the first two elements.

y = gfadd([2 3 1],[4 2 3],5,2)
y = 1×2

1     0

For prime number p and exponent m, create a matrix listing all elements of GF(p^m) given primitive polynomial $2+2x+{x}^{2}$.

p = 3;
m = 2;
primpoly = [2 2 1];
field = gftuple((-1:p^m-2)',primpoly,p);

Sum ${A}^{2}$ and ${A}^{4}$. The result is $A$.