Research

Discrete Mathematics (Leader: Prof. Greg McColm <mccolm (at) usf.edu>document.write('<a href="mai' + 'lto:' + 'mccolm' + '&#64;' + 'usf.edu' + '">Prof. Greg McColm</a>');)

Monday, November 29, 2021

Title: Algebraic Curves over Finite Fields: Theory and Applications
Speaker: Vincenzo Pallozzi Lavorante
Universite degli Studi di Modena e Reggio Emilia
Time: 2:00pm–3:00pm
Place: Zoom Meeting

Abstract

The study of algebraic curves defined over a finite field has attracted much interest in recent times. The purpose of this talk is to introduce the basic notions related to algebraic curves over finite fields, together with some examples of how it finds a concrete and common application in different research areas. In particular we will explore the connection with coding theory, permutation polynomials and see an interesting application in finite geometry.

Monday, November 22, 2021

No seminar this week.

Monday, November 15, 2021

No seminar this week.

Monday, November 8, 2021

No seminar this week.

Monday, November 1, 2021

No seminar this week.

Monday, October 25, 2021

No seminar this week.

Monday, October 18, 2021

No seminar this week.

Monday, October 11, 2021

No seminar this week.

Monday, October 4, 2021

No seminar this week.

Monday, September 27, 2021

No seminar this week.

Monday, September 20, 2021

No seminar this week.

Monday, September 13, 2021

Title: On the Number of Equivalence Classes of Boolean Functions
Speaker: Xiang-dong Hou
Time: 2:00pm–3:00pm
Place: Zoom Meeting

Abstract

Two Boolean functions from $$F_{2^n}$$ to $$F_2$$ are called (affine) equivalent if one can be obtained from the other through an invertible affine transformation of the variables followed by an addition of an affine function. Most coding theoretic and cryptographic properties of Boolean functions are preserved under this equivalence. Let $$N_n$$ denote the number of equivalence classes of Boolean functions in $$n$$ variables. No explicit formula for $$N_n$$ is known. A long-standing open question by MacWilliams and Sloane asks for an asymptotic formula for $$N_n$$ as $$n\to\infty$$. Recently, we found a solution to this question.