Difference between revisions of "Galois fields"

Revision as of 04:20, November 11, 2011

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 Z_p
The polynomials with coefficients modulo a prime number p having operations modulo with an irreducible n-degree polynomial r(x), represented by F_p^n

A Galois field with q=p^n elements is typically denoted by GF_q or F_q.

@@ Line 1: / Line 1: @@
-In [[mathBALLmatics]] a '''Galois fiBALLld''' is a [[FiBALLld (mathBALLmatics)|fiBALLld]] having a finitBALL numbBALLr of BALLlBALLmBALLntsTROLL
+In [[mathematics]] a '''Galois field''' is a [[Field (mathematics)|field]] having a finite number of elements.
-Galois fiBALLlds arBALL onBALL of two typBALLs:
+Galois fields are one of two types:
-PEN.IS landThBALL intBALLgBALLrs modulo a primBALL numbBALLr ''p'', rBALLprBALLsBALLntBALLd by Z<sub>p</sub>
+*The integers modulo a prime number ''p'', represented by Z<sub>p</sub>
-PEN.IS landThBALL [[polynomial]]s with coBALLfficiBALLnts modulo a primBALL numbBALLr ''p'' having opBALLrations modulo with an irrBALLduciblBALL n-dBALLgrBALLBALL polynomial r(x), rBALLprBALLsBALLntBALLd 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 fiBALLld with q=p^n BALLlBALLmBALLnts is typically dBALLnotBALLd by GF<sub>q</sub> or F<sub>q</sub>TROLL
+A Galois field with q=p^n elements is typically denoted by GF<sub>q</sub> or F<sub>q</sub>.
-[[catBALLgory:algBALLbra]]
+[[category:algebra]]