A New Construction of QAM Golay Complementary Sequence Pair
Bibliographic record
Abstract
The previous constructions of quadrature amplitude modulation (QAM) Golay complementary sequences (GCSs) were generalized as 4q-QAM GCSs of length 2mby Li (the generalized cases I-III for q ≥ 2) in 2010 and Liu (the generalized cases IV-V for q ≥ 3) in 2013 respectively. Those sequences are given by the weighted sum of q quaternary standard GCSs, which is represented as q-dimensional vectorial generalized Boolean functions (V-GBFs). In this paper, we present a new construction for 4q-QAM GCSs of length 2m. The new construction includes the generalized cases I-III as special cases. If q is a composite number, a great number of new GCSs other than the sequences in the generalized cases I-V will arise. For the cases q = 4 and q = 6, we show that the ratios of the number of new GCSs and the generalized cases I-V are greater than seven and six respectively if m is large enough.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".