Finite Field with Four Elements

Small note to myself on notational problems when facing finite groups.

Recall the finite field with four elements is ℤ₂[x]/(1+x+x²).

People often write ω = 1+x and ω=x. Observe then that ω² = ω, and ω² = ω. Moreover ωω=1 and 1+ω+ω=0.

I have only seen this ω notation specified in Pless' Error Correcting Codes, Third ed., page 102 et seq.