Find minimal polynomial of Galois field element
pl = minpol(x)
pl = minpol(x) finds
the minimal polynomial of each element in the Galois column vector,
pl is an array in GF(2). The kth row
pl lists the coefficients, in order of descending
powers, of the minimal polynomial of the kth element of
Note: The output is in GF(2) even if the input is in a different Galois field.
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
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.