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SUMMARY:Simultaneous Rational Function Reconstruction and applications to
Algebraic Coding Theory
DTSTART;VALUE=DATE-TIME:20210325T093000Z
DTEND;VALUE=DATE-TIME:20210325T103000Z
DTSTAMP;VALUE=DATE-TIME:20210508T040905Z
UID:indico-event-6544@indico.math.cnrs.fr
DESCRIPTION:The simultaneous rational function reconstruction (SRFR) is th
e problem of reconstructing a vector of rational functions with the same d
enominator given its evaluations (or more generally given its remainders m
odulo different polynomials). The peculiarity of this problem consists in
the fact that the common denominator constraint reduces the number of eval
uation points needed to guarantee the existence of a solution\, possibly l
osing the uniqueness.\n\nOne of the main contributions presented in this t
alk consists in the proof that uniqueness is guaranteed for almost all ins
tances of this problem. This result was obtained by elaborating some other
contributions and techniques derived by the applications of SRFR\, from t
he polynomial linear system solving to the decoding of Interleaved Reed-So
lomon codes.\n\nIn this talk it is also presented another application of t
he SRFR problem\, concerning the problem of constructing fault-tolerant al
gorithms: algorithms resilient to computational errors.\n\nThese algorithm
s are constructed by introducing redundancy and using error correcting cod
es tools to detect and possibly correct errors which occur during computat
ions. In this application context\, we improve an existing fault-tolerant
technique for polynomial linear system solving by evaluation-interpolation
\, by focusing on the related SRFR.\n\nContains joint works with Eleonora
Guerrini and Romain Lebreton.\n\nhttps://indico.math.cnrs.fr/event/6544/
LOCATION:https://bbb.unilim.fr/b/vac-m6r-7dv
URL:https://indico.math.cnrs.fr/event/6544/
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