Trigonometry in Galois Fields - Unimodular Groups

Unimodular Groups

The unimodular set of GI(p), denoted by G₁, is the set of elements ζ = (a + jb) ∈ GI(p), such that a2 + b2 1 (mod p).

To determine the elements of the unimodular group it helps to observe that if ζ = a + jb is one such element, then so is every element in the set ζ = {b + ja, (p − a) + jb, b + j(p − a), a +j(p − b), (p − b) + ja, (p − a) + j(p − b), (p − b) + j(p − a)}.