APM construction · arXiv:2601.08824
Kasai codes
An APM construction that controls permutation-matrix commutativity and breaks the orthogonality barrier in quantum LDPC codes.
The individual-code tables have been restored.
The girth-6/8 instances, parameter files, and minimum-distance and distance upper-bound evaluations are in the Kasai Code Catalog.
The girth-6/8 instances, parameter files, and minimum-distance and distance upper-bound evaluations are in the Kasai Code Catalog.
Classification
Here “Kasai codes” refers specifically to the APM construction in Breaking the Orthogonality Barrier in Quantum LDPC Codes and its individual code instances.
The PP codes in the Okada–Kasai paper, the affine-coset construction, the finite-field two-branch construction, and the rate-2/3 two-branch construction are distinct code families. They are listed separately under PP codes and other QLDPC constructions.
Representative code
A representative example is a girth-8 (3,12)-regular [[9216, 4612, ≤48]] CSS code.
Individual codes and distance evaluation
- Individual-code catalog and live upper-bound table
- P=216 candidate catalog
- P=2688 candidate catalog
- Definitions of the distance upper bounds
- How to read APM parameter files
- Supplementary materials and representative parameter files