Construct a field of 9 elements – construct the addition and multiplication tables. Begin with polynomials having coefficients $0$, $1$, and $2$ (integers modulo $3$) and use the modulus $X^2+X+2$
I really am not sure what its asking. I know how to do the multiple and addition of a field of $9$ but not sure about the rest at all.
Any help? Or even a similar example? Help me understand. Thanks!
Am I being asked to mod the addition and multiplication tables by $\ X^2+X+2 \quad (8) \ $? Am I supposed to write out all possible polynomials with modulo $3$ coefficients and $\mathrm{mod} \ X^2+X+1$?
Make no sense to me.