A locally testable code (LTC) is an error correcting code that has a property-tester. The tester
reads q bits that are randomly chosen, and rejects words with probability proportional to their …

Abstract The family of Reed-Solomon (RS) codes plays a prominent role in the construction
of quasilinear probabilistically checkable proofs (PCPs) and interactive oracle proofs (IOPs) …

A locally testable code (LTC) is an error correcting code with a property tester. The tester
tests if a word is a codeword by reading constant random bits and rejects the word with …

Existing proofs that deduce BPP= P from circuit lower bounds convert randomized
algorithms into deterministic algorithms with a large polynomial slowdown. We convert …

This book introduces important results and techniques in property testing, where the goal is
to design algorithms that decide whether their input satisfies a predetermined property in …

Classical locally recoverable codes, which permit highly efficient recovery from localized
errors as well as global recovery from larger errors, provide some of the most useful codes …

We show that the tensor product of a high-rate globally list recoverable code is
(approximately) locally list recoverable. List recovery has been a useful building block in the …

We develop new list decoding algorithms for Tanner codes and distance-amplified codes
based on bipartite spectral expanders. We show that proofs exhibiting lower bounds on the …

In this work, we continue the search for quantum locally testable codes (qLTCs) of new
parameters by presenting three constructions that can make new qLTCs from old. The first …

In this work, we show new and improved error-correcting properties of folded Reed-Solomon
codes and multiplicity codes. Both of these families of codes are based on polynomials over …