Advancing Coding Theory Through the Lens of Pseudorandomness

This is an exciting time for error-correcting codes (ECC). ECCs are a fundamental tool to protect data from noise, and the past decade has seen a slew of breakthroughs, both theoretical and practical. The goal of the proposed research is to both leverage and extend this exciting progress, in particular in the areas of h'st—rec0very and codes near the Gilbert—Varsham0v bound, by approaching it from the perspective of pseudorandomness.

Pseudorandomness is the study of deterministic objects that "behave like random objects," and is a fundamental area of theoretical computer science. Connections between pseudorandomness and ECCS are not new, and indeed there has been a rich interplay between the two areas. However, as is argued in the Project Description, the time is right to revisit these connections in light of recent coding-theoretic breakthroughs. Doing so will not only make progress in pseudorandomness by leveraging progress in coding theory, but will also lead to further progress in coding theorey by using applications in pseudorandomness to shine a light on important questions in coding theory where current techniques fall short.