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Algebraic Coding and Cryptography
Online Event
ACCESS is a joint effort designed to highlight world-class research in coding theory, cryptography, and related areas and to encourage collaboration among its participants.
ACCESS is a joint effort designed to highlight world-class research in coding theory, cryptography, and related areas and to encourage collaboration among its participants.
Next seminar
October 20
Olav Geil
Aalborg University
Next seminar
October 20
Olav Geil
Aalborg University
Unified Common-Root and Interpolation Bounds Based on Leading Monomial Data
Unified Common-Root and Interpolation Bounds Based on Leading Monomial Data
Abstract
Many problems in coding theory, secret sharing etc. boil down to questions regarding common roots of sets of multivariate polynomials. In this talk we shall explain how insight from such research areas leads to new results in commutative algebra over arbitrary field. More concretely we shall introduce an Interpolation Bound Theorem which has a flavor similar to the footprint bound from Gröbner basis theory, the latter bound estimating the number of common roots. Insight from coding theory and secret sharing leads us to understand that these two bounds are strongly related. Actually, they answer the same problem, but for dual spaces. Various applications of the footprint bound are presented and the relationship between this bound and the Feng-Rao bounds from algebraic geometry codes is discussed.
Biography. Olav Geil is associate professor at Department of Mathematical Sciences, Aalborg University, Denmark. His research interests include algebraic coding theory, secret sharing, quantum codes, and Gröbner basis theory.
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