Normal basis of the finite field F/sub 2/(p-1)p/sup m/ over F/sub 2/

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