Communications Toolbox

minpol

Find the minimal polynomial of an element of a Galois field

Syntax

• pl = minpol(x);
  

Description

pl = minpol(x) finds the minimal polynomial of each element in the Galois column vector x. The output pl is an array in GF(2). The kth row of pl lists the coefficients, in order of descending powers, of the minimal polynomial of the kth element of x.

Note    The output is in GF(2) even if the input is in a different Galois field.

Examples

The code below uses m = 4 and finds that the minimal polynomial of gf(2,m) is just the primitive polynomial used for the field GF(2^m). This is true for any value of m, not just the value used in the example.

• m = 4;
  A = gf(2,m)
  pl = minpol(A)
  

The output is below. Notice that the row vector [1 0 0 1 1] represents the polynomial D^4 + D + 1.

• A = GF(2^4) array. Primitive polynomial = D^4+D+1 (19 decimal)
  
  Array elements = 
  
       2
  
  
  pl = GF(2) array. 
  
  Array elements = 
  
       1     0     0     1     1
  

Another example is in Minimal Polynomials.

See Also

cosets

mask2shift

mldivide