## Constructing a field

Have just finished reading Chapter 4 from “Finite Fields for Computer Scientists and Engineers – Robert J. McEliece”.

I’ve been away from the computer and spend the whole morning scribbling some calculation on constructing a field. Me now understand that when we have an Euclidean domain $D=F_{2}\left [x \right ]$ with for example $p\left (x \right )=x^{4}+x+1$, that $p$ is irreducible because $p\left (0 \right )=1$ and $p\left (1 \right )=1$, so $p\left (x \right )$ has no zeroes in $F_{2}$.

bla bla bla bla … i have many pages of scribbles…

But I’d like to post this tables here just for a quick reminder for me, it’s unfinished but I’ve got the idea so keeping it up here will be useful someday when I forgot about this $F_{2}^{m}$ stuff 😀