Trigonometry in Galois Fields - The Z Plane in A Galois Field

The Z Plane in A Galois Field

The complex Z plane (Argand diagram) in GF(p) can be constructed from the supra-unimodular set of GI(p):

  • The supra-unimodular set of GI(p), denoted Gs, is the set of elements ζ = (a + jb) ∈ GI(p), such that (a2 + b2) −1 (mod p).
  • The structure s,*>, is a cyclic group of order 2(p + 1), called the supra-unimodular group of GI(p).

The elements ζ = a + jb of the supra-unimodular group Gs satisfy (a2 + b2)21 (mod p) and all have modulus 1. Gs is precisely the group of phases .

  • If p is a Mersenne prime (p = 2n − 1, n > 2), the elements ζ = a + jb such that a2 + b2 −1 (mod p) are the generators of Gs.

Read more about this topic:  Trigonometry In Galois Fields

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