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 codes are asymptotically good, which proves the qLDPC conjecture. Moreover, we show that the produced classical LDPC codes are also asymptotically good and locally testable with constant query and soundness parameters, which proves a well-known conjecture in the field of locally testable codes.

翻译：我们研究的经典和量子LDPC代码,是解除产品制造过程中对非同伴团体的固定费率。我们显示,获得的量子LDPC代码的家族无一例外地好,这证明了qLDPC的推测。 此外,我们显示,所生产的典型LDPC代码也无一例外地好,并且可以用不断的查询和正确度参数进行本地测试,这证明是当地可测试代码领域众所周知的推测。