Difference between revisions of "Galois fields"
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| − | In [[mathematics]] a Galois | + | 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 | + | *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: | + | |
| + | [[category:algebra]] | ||
Revision as of 21:30, June 27, 2008
In mathematics a Galois field is a field having a finite number of elements.
Galois fields are one of two types:
- The integers modulo a prime number p, represented by Zp
- The polynomials with coefficients modulo a prime number p having operations modulo with an irreducible n-degree polynomial r(x), represented by Fp^n
A Galois field with q=p^n elements is typically denoted by GFq or Fq.