Towards the Primitive Completely Normal Basis Theorem

Abstract: Let GF(q) be the finite field of cardinality q and GF(q^n) its extension of degree n. A generator of the multiplicative group GF(q^n)^* is called primitive and some x in GF(q^n) whose GF(q)-conjugates span a GF(q)-basis is called normal over GF(q). In 1996, Morgan and Mullen conjectured that for every q and n, there exists some primitive element of GF(q^n) that is normal over GF(q^d) for every d|n. In this talk, we will describe how this conjecture was established when q>n and we will discuss possible improvements. This is joint work with Theodoulos Garefalakis.

Mathematics

Audience: researchers in the topic

Greek Algebra & Number Theory Seminar