Communications Toolbox

Default Primitive Polynomials

This toolbox provides a default primitive polynomial for each extension field. You can retrieve this polynomial using the gfprimdf function. The command

• prim_poly = gfprimdf(m,p); % If m and p are already defined
  

produces the standard row-vector representation of the default minimal polynomial for GF(p^m).

For example, the command below shows that the default primitive polynomial for GF(9) is 2 + x + x², not the polynomial used in List of All Elements of a Galois Field.

• gfprimdf(2,3)
  
  ans =
  
       2     1     1
  

To generate a list of elements of GF(p^m) using the default primitive polynomial, use the command

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

Nonuniqueness of Representations

Converting and Simplifying Element Formats