Noun
normal basis (plural normal bases)
{\displaystyle }
(algebra, field theory) For a given Galois field ????q and a suitable element β, a basis that has the form {β, β, β, ..., β}.
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
β
q
m
=
β
{\displaystyle \beta ^{q^{m}}=\beta }
.