High-dimensional Expansion of Product Codes is Stronger than Robust and Agreement Testability

Understand

We study the coboundary expansion property of product codes called product expansion, which played a key role in all recent constructions of good qLDPC codes.

• It was shown before that this property is equivalent to robust testability and agreement testability for products of two codes with linear distance.
• First, we show that robust testability for product of many codes with linear distance is equivalent to agreement testability.
• Second, we provide an example of product of three codes with linear distance which is robustly testable but not product expanding.