normal basis
normal basis · normal bases
For a given Galois field 𝔽_ 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)}.
Meaning
1 sensesFor 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.
Translations
1 languagesForms
plural: normal bases| Singular | normal basis |
|---|---|
| Plural | normal bases |
irregular