New Construction of Complementary Sequence (or Array) Sets and Complete Complementary Codes
Bibliographic record
Abstract
A new method to construct q-ary complementary sequence sets (CSSs) and complete complementary codes (CCCs) of size N is proposed by using desired para-unitary (PU) matrices.The concept of seed PU matrices is introduced and a systematic approach on how to compute the explicit forms of the functions in constructed CSSs and CCCs from the seed PU matrices is given.A general form of these functions only depends on a basis of the functions from ZN to Zq and representatives in the equivalent class of Butson-type Hadamard (BH) matrices.Especially, the realization of Golay pairs from the our general form exactly coincides with the standard Golay pairs.The realization of ternary complementary sequences of size 3 is first reported here.For the realization of the quaternary complementary sequences of size 4, almost all the sequences derived here are never reported before.Generalized seed PU matrices and the recursive constructions of the desired PU matrices are also studied, and a large number of new constructions of CSSs and CCCs are given accordingly.From the perspective of this paper, all the known results of CSSs and CCCs with explicit GBF form in the literature (except non-standard Golay pairs) are constructed from the Walsh matrices of order 2.This suggests that the proposed method with the BH matrices of higher orders will yield a large number of new CSSs and CCCs with the exponentially increasing number of the sequences of low peak-to-mean envelope power ratio.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| 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) | 0.003 | 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".