Seminar Coding Theory & Cryptography: Olav Geil
Olav Geil, Aalborg University
Three applications of the footprint bound
The footprint bound estimates the number of common zeros of a set of multivariate polynomials when given information about their leading monomials. Although algebraic of nature; in some incidences a purely combinatorial proof of it can be given. Likewise, the Schwartz-Zippel bound (which ought to be called the Ore bound) can be viewed as a corollary to the footprint bound. In this talk we shall discuss three applications of the bound, namely:
(1) one-point geometric Goppa codes,
(2) random network coding,
(3) small-bias spaces.
In the talk we shall touch on the question: "When are algebraic methods useful in mathematics for communication?"
Location: Grosser Hörsaal