Word.ws English Dictionary

normal basis

normal basis noun: 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)}.

Noun

normal basis (plural normal bases)

  1. (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.
    • It is a characterising property of normal bases that #92;beta#123;qᵐ#125;#61;#92;beta.

Forms of normal basis

pluralnormal bases

Words formed from normal basis

  • normal basis theorem
  • primitive normal basis

Questions about normal basis

What does normal basis mean?
Normal basis means 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)}.
What part of speech is normal basis?
Normal basis is a noun.
What is the plural of normal basis?
The plural of normal basis is normal bases.

Words near normal basis in the dictionary

  1. Normacot
  2. normacusine
  3. normaemic
  4. normal
  5. normal bases
  6. normal basis
  7. normal depth
  8. normal depths
  9. normal distribution
  10. normal distributions
  11. normal extension

Source and license

Adapted from Wiktionary: normal basis (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “normal basis.” Word.ws, https://word.ws/normal_basis. Based on Wiktionary, CC BY-SA 4.0.