16.4

1. The most difficult part for me was realizing that one of the more significant issues in GF(2) and GF(4) (maybe GF(2^n) in general?) is finding the additive inverse of an element and not adding two elements together, but I guess it turns out to be the same thing. It takes an extra step.

2. Even though fields in Z_2 are a more natural fit for computers, does that mean that fields Z_2[x] are also? (This next part is all "if I'm not mistaken".) In the text, only a few lines were dealt with: vertical, horizontal, and the line y=x. A line could have the slope of any element in the group. In GF(4), names were given to each element, so I suppose in, say, GF(256), even though most of the elements may have the ring element x in their representation, this is a different x than the one appearing in y=mx+b, so if considering the line through (0,1) and (1, x^2+x+1) on some hypothetical curve, we would obtain y=(x^2+x+1)x. Is that y=x^3+x^2+x? In other words, are the x's the same? I'm leaning towards yes.