238 citations · 421 across the 10 of their papers we have counts for
6 papers · 1 filter
Maximally Extendable Product Codes are Good Coboundary Expanders
Gleb Kalachev, Pavel Panteleev
We investigate the coboundary expansion property of tensor product codes, known as product expansion, which plays an important role in recent constructions of good quantum LDPC cod…
Maximally Extendable Sheaf Codes
Pavel Panteleev, Gleb Kalachev
We study sheaf codes, a type of linear codes with a fixed hierarchical collection of local codes, viewed as a sheaf of vector spaces on a finite topological space we call coded spa…
High-dimensional Expansion of Product Codes is Stronger than Robust and Agreement Testability
Gleb Kalachev
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 t…
Two-sided Robustly Testable Codes
Gleb Kalachev, Pavel Panteleev
We show that the tensor product of two random linear codes is robustly testable with high probability. This implies that one can obtain pairs of linear codes such that their produc…
Asymptotically Good Quantum and Locally Testable Classical LDPC Codes
Pavel Panteleev, Gleb Kalachev
We study classical and quantum LDPC codes of constant rate obtained by the lifted product construction over non-abelian groups. We show that the obtained families of quantum LDPC c…
Quantum LDPC Codes with Almost Linear Minimum Distance
Pavel Panteleev, Gleb Kalachev
We give a construction of quantum LDPC codes of dimension and distance as the code length . Using a product of chain complexes this constructi…