
\begin{abstract}

Elementary techniques for computation in finite fields are presented, at a
level appropriate for an engineering, computer science or mathematical
audience.
%
Second, elementary Galois theory for finite fields is presented at a
level appropriate for undergraduate or beginning graduate students in
mathematics.  For the latter, illustrative properties of a novel
\emph{logarithmic root chart} are developed.
%
Third, linear feedback shift registers are presented in a manner which connects
mathematical theory and engineering practice.
%
Fourth, some techniques for software implementation are outlined: using a
computer algebra system for the general case, and in C for the $p=2$ case.

This paper is an elaboration on lecture notes for a talk given to the Arizona
State University Math Department's Graduate Student Seminar Series in fall of
2003.

Some software-related updates were made January 2013.

\end{abstract}

