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In [[mathematics]] a Galois Field is a [[Field (mathematics)|field]] having a finite number of elements.
In [[mathematics]] a '''Galois field''' is a [[Field (mathematics)|field]] having a finite number of elements.
Galois fields are one of two types:
Galois fields are one of two types:
*The integers modulo a prime number ''p'', represented by Z<sub>p</sub>
*The integers modulo a prime number ''p'', represented by Z<sub>p</sub>
*The polynomials with coefficients modulo a prime number ''p'' having operations modulo with an irreducible n-degree polynomial r(x), represented by F<sub>p^n</sub>
*The [[polynomial]]s with coefficients modulo a prime number ''p'' having operations modulo with an irreducible n-degree polynomial r(x), represented by F<sub>p^n</sub>
A Galois field with q=p^n elements is typically denoted by GF<sub>q</sub> or F<sub>q</sub>.
A Galois field with q=p^n elements is typically denoted by GF<sub>q</sub> or F<sub>q</sub>.
[[category:mathematics]]
[[category:algebra]]