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(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. 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

In the code below, sum5 is the sum of 2 + 3x + x2 and 4 + 2x + 3x2 over GF(5), and linpart is the degree-one part of sum5.

sum5 = gfadd([2 3 1],[4 2 3],5)
linpart = gfadd([2 3 1],[4 2 3],5,2)

The output is

sum5 =

     1     0     4


linpart =

     1     0

The code below shows that A2 + A4 = A1, where A is a root of the primitive polynomial 2 + 2x + x2 for GF(9).

p = 3; m = 2;
prim_poly = [2 2 1];
field = gftuple([-1:p^m-2]',prim_poly,p);
g = gfadd(2,4,field)

The output is

g =

     1

Other examples are in Arithmetic in Galois Fields.

See Also

| | | | |

Was this topic helpful?