English Dictionary

normal basis

名詞

(algebra, field theory) 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)}.

日本語の意味

正規基底：有限体のガロア体拡大 F₍qᵐ₎ において、適切な元 β のガロア共役 {β, β^q, β^(q²), …, β^(q^(m-1))} により構成される基底。

In many coding theory applications, constructing a normal basis of F_{qm} simplifies computations involving Frobenius automorphisms.

多くの符号理論の応用では、F_{q^m} の形が {β, β^q, β^{q^2}, …, β^{q^{m-1}}} となる基底（正規基底）を構成することで、フロベニウス自己同型に関する計算が簡単になる。

意味（1）

(algebra, field theory) 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.

normal bases （ plural ）