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Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that has a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are the…

Applications, Properties & Multiplicative structure

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Overview

Properties

Existence and uniqueness

Explicit construction

Multiplicative structure

Frobenius automorphism and Galois theory

Polynomial factorization

Algebraic closure

Applications

Generalizations

Advanced semantic analysis

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Map overview Semantic statistics

Finite field

Nodes143
Edges142
Triples51
Avg. degree1.99
Density0.013986
Components1

How this topic connects Entity context

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Finite field

Top relations

has application · 15
Finite field → BCH, Diffie, ECDHE, Finite, For, GF, Hellman, In, One, PDF417, Reed, Solomon, Some CPUs, The, Wikipedia
related to Existence and uniqueness · 6
Finite field → Also, GF, In, Let, The, This
is a · 5
Finite field → basis of several widely used protocols, field that is a finite set, prime power, root of unity, set on which the operations of multiplication
related to External links · 5
Finite field → Finite Fields, Open Access Journal, Science Direct, Their Applications, Wolfram
related to GF(p2) for an odd prime p · 5
Finite field → For, GF, If, More, There
related to Generalizations · 4
Finite field → If, The Artin, Wedderburn's, Zorn
related to Algebraic closure · 3
Finite field → Conway, Given, It
related to Roots of unity · 3
Finite field → Every, GF, If
related to Polynomial factorization · 2
Finite field → As, If
related to Properties · 2
Finite field → In, The

Important terminology Word statistics

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Important terminology

displaystyle field gf finite mathrm polynomial elements fields irreducible roots number order polynomials prime element degree one primitive characteristic may

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Finite fieldis aset on which the operations of multiplication0.90text
Finite fieldis afield that is a finite set0.90text
Finite fieldis aprime power0.90text
Finite fieldis aroot of unity0.90text
Finite fieldis abasis of several widely used protocols0.90text
Finite fieldhas applicationIn0.60section
Finite fieldhas applicationDiffie0.60section
Finite fieldhas applicationHellman0.60section
Finite fieldhas applicationFor0.60section
Finite fieldhas applicationWikipedia0.60section
Finite fieldhas applicationECDHE0.60section
Finite fieldhas applicationFinite0.60section

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