Bibliographic record
Abstract
Golay pairs (GPs) are pairs of (1,-1)-sequences with zero autocorrelation. GPs have numerous applications in engineering and mathematics such as in device synchronization, spectroscopy, and in the construction of Hadamard matrices. As a result, there is significant interest in understanding their mathematical structure. However, the structure of GPs appears to be very mysterious. Ternary complementary pairs (TCPs)—a generalization of GPs—are pairs of (0,1,-1)-sequences with zero autocorrelation. Similar to GPs, the structure of TCPs appears to be quite challenging. In order to gain insight into TCPs and GPs, Craigen introduced Boolean complementary pairs (BCPs), which are pairs of Z_2-sequences with zero autocorrelation. Craigen solved the structure of even-weight BCPs and with Woodford discovered a factorization involving 2x2 matrices in the odd-weight case. A review of Golay pairs, ternary complementary pairs, and Boolean complementary pairs is given. The odd-weight BCP factorization is extended to all pairs of Z_2-sequences with zero autocorrelation. Consequences of this extension are then established, including a connection to affixes.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.025 | 0.007 |
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".