New designs for signal sets with low cross correlation, balance property, and large linear span: GF(p) case
Bibliographic record
Abstract
New designs for families of sequences over GF(p) with low cross correlation, balance property, and large linear span are presented. The key idea of the new designs is to use short p-ary sequences of period /spl upsi/ with the two-level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties. The resulting sequences are interleaved sequences of period /spl upsi//sup 2/. There are /spl upsi/ cyclically shift distinct sequences in each family. The maximal correlation value is 2/spl upsi/ + 3 which is optimal with respect to the Welch bound. Each sequence in the family is balanced and has large linear span. In particular, for binary case, cross/out-of-phase autocorrelation values belong to the set {1, -/spl upsi/, /spl upsi/ + 2, 2/spl upsi/ + 3, -2/spl upsi/ - 1}, any sequence where the short sequences are quadratic residue sequences achieves the maximal linear span. It is shown that some families of these sequences can be implemented efficiently in both hardware and software.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".