Article collection "Mathematical Problems of Cybernetics" №21, Moscow, 2023
Authors:Kalachev G.V., Panteleev P.A.
Asymptotically good families of quantum and locally testable classical LDPC codes
Abstract:
In this paper we study classical and quantum LDPC codes with constant rate obtained using tensor product operation over noncommutative group algebra for chain complexes. It is shown that these families of quantum LDPC codes are asymptotically good, which proves the qLDPC conjecture. The existence of asymptotically good families of locally testable codes with constant parameters of locality and soundness is also shown, which gives the solution of the known conjecture in the field of classical locally testable codes.
