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Weil sums of binomials: properties and applications (Daniel Katz, CSUN)

November 27, 2018 @ 12:15 pm - 1:10 pm

We consider sums in which an additive character of a finite field F is applied to a binomial whose individual terms (monomials) become permutations of F when regarded as functions.  These Weil sums characterize the nonlinearity of power permutations of interest in cryptography.  They also tell us about the correlation of linear recursive sequences over finite fields that are used in digital communications and remote sensing.  In these applications, one is interested in the spectrum of Weil sum values that are obtained as the coefficients in the binomial are varied.  We discuss topics of enduring interest: Archimedean and non-Archimedean bounds on the sums, the number of values in the spectrum, and the presence or absence of zero in the spectrum.  We indicate some important open problems and discuss progress that has been made on them.

Details

Date:
November 27, 2018
Time:
12:15 pm - 1:10 pm
Event Category:

Organizer

Lenny Fukshansky

Other

Speaker Name
Daniel Katz (CSUN)

Venue

Millikan 2099, Pomona College
610 N. College Ave.
Claremont, CA 91711 United States
+ Google Map

Details

Date:
November 27, 2018
Time:
12:15 pm - 1:10 pm
Event Category:

Organizer

Lenny Fukshansky

Other

Speaker Name
Daniel Katz (CSUN)

Venue

Millikan 2099, Pomona College
610 N. College Ave.
Claremont, CA 91711 United States
+ Google Map