Improved quantum hypergraph-product LDPC codes
Abstract
We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Z\'emor. For the usual toric codes, we introduce the rotated lattices specified by two integer-valued periodicity vectors. These codes include the checkerboard codes, and the family of minimal single-qubit-encoding toric codes with block length n=t2+(t+1)2 and distance d=2t+1, t=1,2,.... We also suggest several related algebraic constructions which nearly quadruple the rate of the existing hypergraph-product codes.
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