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,
x. The output
pl is an array in GF(2). The kth row of
lists the coefficients, in order of descending powers, of the minimal polynomial of
the kth element of
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
gf(2,m) is just the primitive polynomial used for the field
2^m). This is true for any value of
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.