Error-correcting codes in complexity theory

Abstract

Error-correcting codes and related combinatorial constructs play an important role is several recent (and old) results in complexity theory. This course will give a brief overview of the theory, constructions, algorithms, and applications of error-correcting codes.We will begin with basic definitions and the constructions of Reed-Solomon, Reed-Muller, and low-weight parity-check codes, then see unique-decoding and listdecoding algorithms, and finally, as time allows, applications to secretsharing, hashing, private information retrieval, average-case complexity and probabilistically checkable proofs.