Wir nehmen die Darstellung

${\displaystyle {\mathbb {F} }_{25}\cong {\mathbb {F} }_{5}[X]/(X^{2}+X+2)}$.

Dabei ist ${\displaystyle X^{2}+X+2}$ irreduzibel in ${\displaystyle {\mathbb {F} }_{5}[X]}$, da es keine Nullstelle in ${\displaystyle {\mathbb {F} }_{5}}$ besitzt. Es bezeichne ${\displaystyle x}$ die Restklasse von ${\displaystyle X}$.

${\displaystyle +}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 0}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 1}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 2}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 3}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle x}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle x+1}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle x+2}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle x+3}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle x+4}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 2x}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle 2x+1}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle 2x+2}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle 2x+3}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle 2x+4}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle 3x}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 3x+1}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 3x+2}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 3x+3}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 3x+4}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 4x}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 4x+1}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 4x+2}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 4x+3}$

${\displaystyle 4x+3}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle x+3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle 2x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 3x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 4x+4}$

${\displaystyle 4x+4}$

${\displaystyle 4x}$

${\displaystyle 4x+1}$

${\displaystyle 4x+2}$

${\displaystyle 4x+3}$

${\displaystyle 4}$

${\displaystyle 0}$

${\displaystyle 1}$

${\displaystyle 2}$

${\displaystyle 3}$

${\displaystyle x+4}$

${\displaystyle x}$

${\displaystyle x+1}$

${\displaystyle x+2}$

${\displaystyle x+3}$

${\displaystyle 2x+4}$

${\displaystyle 2x}$

${\displaystyle 2x+1}$

${\displaystyle 2x+2}$

${\displaystyle 2x+3}$

${\displaystyle 3x+4}$

${\displaystyle 3x}$

${\displaystyle 3x+1}$

${\displaystyle 3x+2}$

${\displaystyle 3x+3}$