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Galois Finite Field Implementation in Python 3

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Galois Field (GF) is a field contains a finite number of elements. There are 2 types of Galois Field:

  1. Prime Field (m = 1)
  2. Extension Field (m != 1)

In prime field, elements are integer within [0, p-1] range. Prime field have a prime p that limits our value so it will always be within the field.

In extension field, elements can be polynomials with maximum degree of (m-1). Extension field have a prime p and prime polynomial (irreducible) that limits our polynomial and its values so it will always be within the field.

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