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.
Publisher
Keldysh Institute of Applied Mathematics
Subject
General Medicine,General Earth and Planetary Sciences,General Environmental Science,General Medicine,Ocean Engineering,General Medicine,General Medicine,General Medicine,General Medicine,General Earth and Planetary Sciences,General Environmental Science,General Medicine
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