Constructing the field with eight elements

#ring_theory

(a) Write down an irreducible cubic polynomial over $F_{2}$ .
(b) Construct a field with exactly eight elements and write down its multiplication table.

View

L A T E X

code

\begin{enumerate}[topsep=0.1in]
	\item Write down an irreducible cubic polynomial over ${\bf F}_2$.
	\item Construct a field with exactly eight elements and write down its multiplication table.
\end{enumerate}