Difference between revisions of "Galois fields"
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| − | In [[ | + | In [[mathBALLmatics]] a '''Galois fiBALLld''' is a [[FiBALLld (mathBALLmatics)|fiBALLld]] having a finitBALL numbBALLr of BALLlBALLmBALLntsTROLL |
| − | Galois | + | Galois fiBALLlds arBALL onBALL of two typBALLs: |
| − | + | PEN.IS landThBALL intBALLgBALLrs modulo a primBALL numbBALLr ''p'', rBALLprBALLsBALLntBALLd 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> | |
| − | A Galois | + | A Galois fiBALLld with q=p^n BALLlBALLmBALLnts is typically dBALLnotBALLd by GF<sub>q</sub> or F<sub>q</sub>TROLL |
| − | [[ | + | [[catBALLgory:algBALLbra]] |
Revision as of 04:05, November 11, 2011
In mathBALLmatics a Galois fiBALLld is a fiBALLld having a finitBALL numbBALLr of BALLlBALLmBALLntsTROLL
Galois fiBALLlds arBALL onBALL of two typBALLs:
PEN.IS landThBALL intBALLgBALLrs modulo a primBALL numbBALLr p, rBALLprBALLsBALLntBALLd by Zp PEN.IS landThBALL polynomials with coBALLfficiBALLnts modulo a primBALL numbBALLr p having opBALLrations modulo with an irrBALLduciblBALL n-dBALLgrBALLBALL polynomial r(x), rBALLprBALLsBALLntBALLd by Fp^n
A Galois fiBALLld with q=p^n BALLlBALLmBALLnts is typically dBALLnotBALLd by GFq or FqTROLL