Faruk Goeloglu

will speak on

Kloosterman-Like Sums with Moebius Inversion

Time: 4:00PM
Date: Mon 25th January 2010
Location: Mathematical Sciences Seminar Room [map]

Abstract: We give divisibility results on Kloosterman-like sums using Numerical Normal Form (NNF). A Kloosterman sum $K_n(a)$ is an exponential sum related to the Walsh transform $W_f(a)$ of the inverse function $f=x^{-1}$ on $GF(2^n)$, which is of degree $n-1$. Helleseth and Zinoviev proved that $K_n(a)$ 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 $W_f(a)$ is divisible by $8$ if and only if $a$ is in some fixed hyperplane.

(This talk is part of the Algebra and Number Theory series.)

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