The primitive normal basis theorem asks whether every finite field extension has a primitive normal basis of this extension. The proof of this problem has recently been completed by Lenstra and Schoof (1987) , and another proof is given by Cohen and Huczynska (2003) . We present a more general result, where the primitive element generating a normal basis is replaced by a primitive element generating the finite Carlitz module. Such generators always exist except for finitely many cases which might not exist.
- Character sum over finite fields
- Finite Carlitz modules
- Primitive roots
ASJC Scopus subject areas
- Algebra and Number Theory