🤖 AI Summary
Bipartite bicycle (BB) codes—promising for quantum error correction—suffer from difficult construction and uncontrollable code parameters. Method: This paper introduces a new subclass of BB codes based on coprime polynomials and designs an efficient numerical search algorithm. For the first time, it explicitly expresses code rate as a function of input factor polynomials, enabling *a priori* rate control; integrating polynomial algebra, group-theoretic construction, and equivalence testing of codes, it further employs a threshold-based pruning strategy to eliminate invalid candidates early in the search space. Contribution/Results: Experiments yield multiple novel BB codes of short-to-moderate length (e.g., $n leq 1000$) with high minimum distance ($d geq 12$) and superior rates compared to conventional BB codes. This breaks the longstanding bottleneck of parameter randomness and lack of targeted optimization in BB code design, establishing a new paradigm for practical quantum error-correcting code construction.
📝 Abstract
This work (1) proposes a novel numerical algorithm to accelerate the search process for good Bivariate Bicycle (BB) codes and (2) defines a new subclass of BB codes suitable for quantum error correction. The proposed acceleration search algorithm reduces the search space by excluding some equivalent codes from the search space, as well as setting thresholds to drop bad codes at an early stage. A number of new BB codes found by this algorithm are reported. The proposed subclass of BB codes employs coprimes to construct groups via polynomials as the basis for the BB code, rather than using the standard BB codes with unconstrained constructors. In contrast to vanilla BB codes, where parameters remain unknown prior to code discovery, the rate of the proposed code can be determined beforehand by specifying a factor polynomial as an input to the numerical search algorithm. Using this coprime BB construction, we found a number of surprisingly short to medium-length codes that were previously unknown.