The peak sidelobe level of families of binary sequences
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Bibliographic record
Abstract
A numerical investigation is presented for the peak sidelobe level (PSL) of Legendre sequences, maximal length shift register sequences (m-sequences), and Rudin-Shapiro sequences. The PSL gives an alternative to the merit factor for measuring the collective smallness of the aperiodic autocorrelations of a binary sequence. The growth of the PSL of these infinite families of binary sequences is tested against the desired growth rate o(/spl radic/nlnn) for sequence length n. The claim that the PSL of m-sequences grows like O(/spl radic/n), which appears frequently in the radar literature, is concluded to be unproven and not currently supported by data. Notable similarities are uncovered between the PSL and merit factor behavior under cyclic rotations of the sequences.
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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 | 0.000 | 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 | 0.001 |
| Open science | 0.000 | 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 it