normal basis

Definitions

1. 1

   For a given Galois field 𝔽_(qᵐ) and a suitable element β, a basis that has the form {β,…

   For a given Galois field 𝔽_(qᵐ) and a suitable element β, a basis that has the form {β, β^q, β^(q2), ... , β^(qm-1)}.

   • A normal basis is generated by the repeated action of the Frobenius endomorphism on a suitable element β; it is the orbit of β for that endomorphism.
   • It is a characterising property of normal bases that #92;beta#123;qᵐ#125;#61;#92;beta.

The neighborhood