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

Add Two GF Arrays

Sum $$2+3x+x^2$$ and $$4+2x+3x^2$$ 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 $$A$$.

g = gfadd(2,4,field)

g = 
1

Version History

Introduced before R2006a