Improved quantum hypergraph-product LDPC codes

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 Zémor. 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 = t
²
+ (t+1)
²
and distance d = 2t + 1, t = 1, 2, ... We also suggest several related algebraic constructions which increase the rate of the existing hypergraph-product codes by up to four times.