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

Kalachev Gleb Vyacheslavovich

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

Kalachev G. V.

Kalachev Gleb Vyacheslavovich

Candidate of Physical and Mathematical Sciences, Researcher, Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Chair of Mathematical Theory of Intellectual Systems

0000-0003-2695-3179

Received: 06 Mar 2026 Accepted: 16 Jun 2026

Published: 2026, vol. 30, issue 2, pp. 101–119

Download full text (In Russian)

Abstract

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 the product of many codes with linear distance is equivalent to agreement testability. Second, we provide an example of the product of three codes with linear distance that is robustly testable but not product expanding.

Keywords: tensor product code, coboundary expansion, robust testability, agreement testability.

BibTeX

@article{IS-Kalachev2026,
  author  = {Kalachev, Gleb Vyacheslavovich},
  title   = {{High-Dimensional Expansion of Product Codes is Stronger than Robust and Agreement Testability}},
  journal = {Intelligent Systems. Theory and Applications},
  year    = {2026},
  volume  = {30},
  number  = {2},
  pages   = {101--119},
}

AMSBIB

\Bibitem{IS-Kalachev2026}
\by G.\,V.~Kalachev
\paper High-Dimensional Expansion of Product Codes is Stronger than Robust and Agreement Testability
\jour Intelligent Systems. Theory and Applications
\yr 2026
\vol 30
\issue 2
\pages 101--119
\lang In Russian

Published under Creative Commons Attribution 4.0 International (CC BY 4.0)

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