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gptkbp:instanceOf
|
finite field
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gptkbp:additive_group
|
abelian group of order q
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gptkbp:alsoKnownAs
|
gptkb:Galois_field
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gptkbp:application
|
gptkb:geometry
error-correcting codes
pseudorandom number generation
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gptkbp:automorphismGroup
|
cyclic of order n, where q=p^n
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gptkbp:characteristic
|
prime divisor of q
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gptkbp:every_element_satisfies
|
x^q = x
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gptkbp:exists_if_and_only_if
|
q is a prime power
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gptkbp:extension_of
|
F_p
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gptkbp:Frobenius_automorphism
|
x ↦ x^p
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gptkbp:hasSubfield
|
fields F_{p^d} for d dividing n
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
finite field F q
|
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gptkbp:minimal_polynomial
|
irreducible polynomial of degree n over F_p
|
|
gptkbp:multiplicative_group
|
cyclic group of order q-1
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gptkbp:notation
|
gptkb:GF(q)
F_q
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|
gptkbp:number_of_elements
|
q
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|
gptkbp:order
|
q
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|
gptkbp:primitive_element
|
exists
|
|
gptkbp:splitting_field_of
|
x^{q}-x over F_p
|
|
gptkbp:structure
|
simple field
|
|
gptkbp:unique_up_to_isomorphism
|
yes
|
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gptkbp:used_in
|
gptkb:algebraic_geometry
coding theory
cryptography
combinatorics
|
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gptkbp:bfsParent
|
gptkb:SL(n,q)
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gptkbp:bfsLayer
|
7
|