Abstract
This introductory chapter contains some basic results on bases for finite fields that will be of interest or use throughout the book. The concentration is on the existence of certain types of bases, their duals and their enumeration. There has been considerable activity in this area in the past decade and while many of the questions are resolved, a few of the important ones remain open. The presentation here tries to complement that of Lidl and Niederreiter [21] although there is some unavoidable overlap. For a more extensive treatment of the topics covered in this chapter, we recommend the recent book by D. Jungnickel [15]. For the remainder of this section some basic properties of the trace and norm functions are recalled.
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