On: Galois field instructions on 2021 CPUs

[sbf501]

Ah, thanks! Fields are a lot less intimidating than I thought they would be! Well, I mean: the basic idea (after reading these replies + wikipedia).

[vmilner → sbf501]

There is a finite field (or Galois field GF(p)) of size p for any prime p. This can be exhibited by integers mod p.

There are also finite (Galois) fields GF(p^n) of size p^n (positive integer powers of p)

These can be exhibited by polynomials with coefficients in the GF(p) field with up to n terms.

Eg for p = 2 and n = 3

0

1

x

1 + x

1 + x + x^2

1 + x^2

x + x^2

x^2