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 😀