On the Perfect Cyclically Conjugated Even and Odd Periodic Autocorrelation Properties of Quaternary Golay Sequences
Bibliographic record
Abstract
A sequence is called perfect if its autocorrelation function is a delta function. In this paper, we give a new definition of autocorrelation function: generalized even and odd periodic autocorrelation, and generalized even and odd periodic cyclically conjugated autocorrelation. In particular, we study a special case of autocorrelation function called cyclically conjugated autocorrelation function. As a result, we present several classes of perfect cyclically conjugated even periodic and odd periodic autocorrelation of quaternary Golay sequences. We also considered such perfect property for 4q-QAM Golay sequences, q ≥ 2 being an integer. Those proposed sequences could be used for synchronization and detection if the time delay is known. Index Terms. Golay sequence, quadrature amplitude modulation (QAM), cyclically conjugated even periodic autocorrelation, cyclically conjugated odd periodic autocorrelation. 1
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".