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gptkbp:instanceOf
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gptkb:finite_field
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gptkbp:additive_group
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abelian group of order q
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gptkbp:alsoKnownAs
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gptkb:Galois_field
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gptkbp:application
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gptkb:geometry
error-correcting codes
pseudorandom number generation
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gptkbp:automorphismGroup
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cyclic of order n, where q=p^n
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gptkbp:characteristic
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prime divisor of q
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gptkbp:every_element_satisfies
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x^q = x
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gptkbp:exists_if_and_only_if
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q is a prime power
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gptkbp:extension_of
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F_p
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gptkbp:Frobenius_automorphism
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x ↦ x^p
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gptkbp:hasSubfield
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fields F_{p^d} for d dividing n
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gptkbp:minimal_polynomial
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irreducible polynomial of degree n over F_p
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gptkbp:multiplicative_group
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cyclic group of order q-1
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gptkbp:notation
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gptkb:GF(q)
F_q
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gptkbp:number_of_elements
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q
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gptkbp:order
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q
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gptkbp:primitive_element
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exists
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gptkbp:splitting_field_of
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x^{q}-x over F_p
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gptkbp:structure
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simple field
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gptkbp:unique_up_to_isomorphism
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yes
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gptkbp:used_in
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gptkb:combinatorics
gptkb:algebraic_geometry
coding theory
cryptography
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gptkbp:bfsParent
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gptkb:symplectic_group_over_finite_fields
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gptkbp:bfsLayer
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9
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https://www.w3.org/2000/01/rdf-schema#label
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finite field F q
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