Normal basis of the finite field F2(p-1)pm over F2

The determination of normal bases for finite fields, particularly over the finite field F₂, is of importance in applications such as coding and cryptography. This correspondence gives an explicit normal basis for a finite field F₂(p-1)p^m over F ₂, when 2 is a primitive element module p². In the case when p=3, an explicit dual basis is also obtained