On existence of canonical GG-bases

We describe a general method for expanding a truncated G-iterative Hasse-Schmidt derivation, where G is an algebraic group. We give examples of algebraic groups for which our method works

A Polylogarithmic PRG for Degree 22 Threshold Functions in the Gaussian Setting

We devise a new pseudorandom generator against degree 2 polynomial threshold functions in the Gaussian setting. We manage to achieve $\epsilon$ error with seed length polylogarithmic in $\epsilon$ and the dimension, and exponential improvement over previous constructions

A Pseudorandom Generator for Polynomial Threshold Functions of Gaussian with Subpolynomial Seed Length

We develop a pseudorandom generator that fools degree-$d$ polynomial threshold functions in $n$ variables with respect to the Gaussian distribution and has seed length $O_{c,d}(\log(n) \epsilon^{-c})$

Perfect single error-correcting codes in the Johnson Scheme

Delsarte conjectured in 1973 that there are no nontrivial pefect codes in the Johnson scheme. Etzion and Schwartz recently showed that perfect codes must be k-regular for large k, and used this to show that there are no perfect codes correcting single errors in J(n,w) for n <= 50000. In this paper we show that there are no perfect single error-correcting codes for n <= 2^250.Comment: 4 pages, revised, accepted for publication in IEEE Transactions on Information Theor