Friday, May 18, 2012

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.

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