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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

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