Girth Analysis of Quantum Quasi-Cyclic LDPC Codes
Bibliographic record
Abstract
Quantum quasi-cyclic LDPC (QQC LDPC) codes, as CSS (Calderbank, Shor, and Steane) codes, are attracting attention because of their good structure and popular channel coding schemes. Fully connected quasi-cyclic LDPC (QC-LDPC) codes with different girths which result in QQC-LDPC codes are investigated. We analytically prove that QC-LDPC codes with column weight at least 3, which yield a QQC-LDPC code, have girth at most 6. To obtain a QQC-LDPC code from QC-LDPC codes with girth more than 6 we should focus on QC-LDPC codes with column weight 2. We present an efficient and practical method to construct these codes with girth at least 8. Then, we extend our method to construct codes with column weight 2 and girth 12, thus reaching the largest possible girth.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".