Rate Adjustable Bivariate Bicycle Codes for Quantum Error Correction

This work (1) proposes a novel numerical algorithm to accelerate the search process for good Bivariate Bicycle (BB) codes and (2) defines a new variant of BB codes suitable for quantum error correction. In contrast to vanilla BB codes, where parameters remain unknown prior to code discovery, the rate of the proposed code can be determined before the search by specifying a factor polynomial. A number of new BB codes found by this algorithm are reported. In particular, by using the proposed construction of BB codes, we found a number of surprisingly short to medium-length codes that were previously unknown.