Coboundary Expansion of Tensor Product Codes over Large Fields

Abstract

The coboundary expansion property of tensor product codes, also known as product expansion, plays an important role in the discovery of good quantum LDPC codes and classical locally testable codes. Prior research has shown that this property is equivalent to agreement testability and robust testability for products of two codes with linear distance. However, for products of more than two codes, it is a strictly stronger property.

In this talk, I will outline key ideas underlying a recent result establishing that tensor products of an arbitrary number of random codes over sufficiently large fields exhibit strong coboundary expansion. This result suggests promising directions for new quantum locally testable code constructions.