A TOWER OF ARTIN-SCHREIER EXTENSIONS OF FINITE FIELDS AND ITS APPLICATIONS
We study a tower of Artin-Schreier extensions of finite fields. Using this tower, we construct a huge finite field of order
?for arbitrary
?without any primitive element, and we give an algorithm for multiplication of two elements in vector expression. We will also discuss the primitivity of some elements in a finite field with the relationship to Fermat numbers.
finite fields, Artin-Schreier extension, Fermat numbers.
