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Q: Construct GF(4). Verify (1+α)² where α²+α+1 = 0. GF(4) = {0, 1, α, 1+α}, α² = α+1 (char 2: α+α = 0!). (1+α)² = 1+2α+α² = 1+α² (char 2!) = 1+α+1 = α. Check: (1+α)³ = (1+α)α = α+α² = α+α+1 = 1 ✓! Multiplicative group: cyclic order 3!