Extracting Information from a Galois Array :: Galois Field Computations (Communications Toolbox)

Communications Toolbox

Extracting Information from a Galois Array

To extract the array elements, field order, or primitive polynomial from a variable that is a Galois array, append a suffix to the name of the variable. The table below lists the exact suffixes, which are independent of the name of the variable.

Information	Suffix	Output Value
Array elements	`.x`	MATLAB array of type `uint16` that contains the data values from the Galois array
Field order	`.m`	Integer of type `double` that indicates that the Galois array is in GF(`2^m`)
Primitive polynomial	`.prim_poly`	Integer of type `uint32` that represents the primitive polynomial. The representation is similar to the description in How Integers Correspond to Galois Field Elements.

Note If the output value is an integer data type and you want to convert it to double for later manipulation, use the double function.

The code below illustrates the use of these suffixes. The definition of empr uses a vector of binary coefficients of a polynomial to create a Galois array in an extension field. Another part of the example retrieves the primitive polynomial for the field and converts it to a binary vector representation having the appropriate number of bits.

% Check that e solves its own minimal polynomial.
e = gf(6,4); % An element of GF(16)
emp = minpol(e); % The minimal polynomial, emp, is in GF(2).
empr = roots(gf(emp.x,e.m)); % Find roots of emp in GF(16).

% Check that the primitive element gf(2,m) is
% really a root of the primitive polynomial for the field.
primpoly_int = double(e.prim_poly);
mval = e.m;
primpoly_vect = gf(de2bi(primpoly_int,mval+1,'left-msb'),mval);
containstwo = roots(primpoly_vect); % Output vector includes 2.

Determining Whether a Variable Is a Galois Array

Speed and Nondefault Primitive Polynomials