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 >>>

Pseudorandom generators (PRGs) for low-degree polynomials are a central object in pseudorandomness, with applications to circuit lower bounds and derandomization. Viola’s celebrated construction (CC 2009) gives a PRG over the binary field, but with seed length exponential in the degree $d$. This exponential dependence can be avoided over sufficiently large ... more >>>

One of the oldest problems in coding theory is to match the Gilbert--Varshamov bound with explicit binary codes. Over larger---yet still constant-sized---fields, algebraic-geometry codes are known to beat the GV bound. In this work, we leverage this phenomenon by taking traces of AG codes. Our hope is that the margin ... more >>>