This is a survey of pseudorandomness, the theory of efficiently generating objects that" look
random" despite being constructed using little or no randomness. This theory has …

Proving circuit lower bounds has been an important but extremely hard problem for
decades. Although it can be shown that almost every function f: F2 n→ F2 requires circuit of …

A long line of work in the past two decades or so established close connections between
several different pseudorandom objects and applications, including seeded or seedless non …

We give an introduction to the area of “randomness extraction” and survey the main
concepts of this area: deterministic extractors, seeded extractors and multiple sources …

In a recent breakthrough [1], Chattopadhyay and Zuckerman gave an explicit two-source
extractor for min-entropy k≥ log C n for some large enough constant C, where n is the …

We study the behavior of the multiplicative inverse function (which plays an important role in
cryptography and in the study of finite fields), with respect to a recently introduced …

Subspace codes have received an increasing interest recently due to their application in
error correction for random network coding. In particular, cyclic subspace codes are possible …

We obtain the first deterministic extractors for sources generated (or sampled) by small
circuits of bounded depth. Our main results are (1) we extract k(k/nd)^O(1) bits with …

Subspace codes and particularly constant dimension codes have attracted much attention in
recent years due to their applications in random network coding. As a particular subclass of …

We consider the repair problem for Reed–Solomon (RS) codes, evaluated on an-linear
subspace of dimension, where is a prime power, is a positive integer, and is the Galois field …