A subspace design is a collection of subspaces $H_1,\ldots,H_n$ of $\mathbb{F}_q^k$ with the property that no low-dimensional subspace $W$ intersects the collection ``too much’’. Subspace designs and related objects in linear-algebraic pseudorandomness have found a broad range of applications, ranging from list decoding and recovery, to derandomizing algorithms.

We ... more >>>

Motivated by recent constructions and barriers in secret sharing, we study multislice functions. These functions, parametrized by a width parameter $w$, take the value 0 on inputs of Hamming weight below a base value $k$, 1 on inputs of weight above $k+w$, and are monotone in between.
We first investigate ... more >>>

We consider the problem of deterministically factoring integers provided with oracle access to important number-theoretic functions such as Euler's Totient function - phi(.) and Carmichael's Lambda function - lambda(.).
We focus on Carmichael numbers - also known as Fermat pseudoprimes. In particular, we obtain the following results:

1. Let N ... more >>>