Extension of finite field F can be considered as a vector space over F and it has a many basis. Normal basis are of the special importance since multiplication of the elements of finite field can be realized in much easier way that in other basis. These are the reasons why normal basis are used in hardware realisation, cryptography and coding theory. Here we will give the definition, characterization and the number of normal basis and introduce some special cases as optimal normal basis with the best possible performance.

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