Kloosterman-Like Sums with Moebius Inversion

Speaker: Faruk Goeloglu

Time: 4:00PM
Date: Mon 25th January 2010

Location: Mathematical Sciences Seminar Room

We give divisibility results on Kloosterman-like sums using Numerical Normal Form (NNF). A Kloosterman sum Kn(a) is an exponential sum related to the Walsh transform Wf(a) of the inverse function f=x−1 on GF(2n), which is of degree n−1. Helleseth and Zinoviev proved that Kn(a) is divisible by 8 if and only if a is in Trace-0-hyperplane. We can use the NNF, a Moebius inversion of a Boolean function, to give a purely combinatorial proof that any Boolean function f with degree n−1 satisfies Wf(a) is divisible by 8 if and only if a is in some fixed hyperplane.

(This talk is part of the Algebra/Claude Shannon Institute series.)