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.
- Pub Date:
- November 2021
- Computer Science - Information Theory;
- Quantum Physics
- Updated the introduction, corrected some misprints, clarified some proofs, added some new bibliography including arXiv:2005.01045 containing an independent construction of good LTCs