Discrete Math Seminar: Daniel Katz

Abstract:

In 1976 Helleseth proposed a beautiful conjecture that connects number theory (Weil sums of binomials), sequence design (cross-correlation of maximum-length sequences), coding theory (weights in sums of irreducible cyclic codes), cryptography (Fourier spectra of power permutations), and finite projective geometry (sizes of intersections between hyperplanes and quadrics). We shall chart the course taken in settling this problem in characteristict wo, the three landmarks being the insight of Calderbank-McGuire-Poonen-Rubinstein, the advance of Feng, and the speaker's proof of the conjecture.