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cs.CC2020
Polynomial time deterministic identity testingalgorithm for circuits via Edelstein-Kelly type theorem for quadratic polynomials
Shir Peleg, Amir Shpilka
In this work we resolve conjectures of Beecken, Mitmann and Saxena [BMS13] and Gupta [Gup14], by proving an analog of a theorem of Edelstein and Kelly for quadratic polynomials. As…
cs.CC2020
A generalized Sylvester-Gallai type theorem for quadratic polynomials
Shir Peleg, Amir Shpilka
In this work we prove a version of the Sylvester-Gallai theorem for quadratic polynomials that takes us one step closer to obtaining a deterministic polynomial time algorithm for t…
cs.IT2020
Reed-Muller Codes: Theory and Algorithms
Emmanuel Abbe, Amir Shpilka, Min Ye
Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and c…