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Coding Theory : How do I compute the addition and multiplication tables for Z mod 2 [x] / (1+x^2)?

How do I compute the addition and multiplication tables for:

Z mod 2 [x] / (1+x^2)?

z mod 2 [x] = 1
z mod 2 [x] = 0
z mod 2 [x] = 1+x
z mod 2 [x] = 1+ x + x^2

I think that 1+ x^2 = 0 so x^2 = -1.

Thats as far as I got.

Solution Preview

All the elements in Z mod 2[x]/(1+x^2) are
0, 1, x, and 1+x
Since 1+x^2=0, then 1+x+x^2=x.
So the addition table is
0 ...

Solution Summary

Addition and multiplication tables are computed for Z mod 2 [x] / (1+x^2). The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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