Combinatorial Constructions for Optimal Two-Dimensional Optical Orthogonal Codes
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Bibliographic record
Abstract
Optical orthogonal codes (OOCs) have been designed for OCDMA. A one-dimensional (1-D) optical orthogonal code (1-D OOC) is a set of one-dimensional binary sequences having good auto and cross-correlations. One limitation of 1-D OOC is that the length of the sequence increases rapidly when the number of users or the weight of the code is increased, which means large bandwidth expansion is required if a big number of codewords is needed. To lessen this problem, two-dimensional (2-D) coding (also called multiwavelength OOCs) was invested. A two dimensional (2-D) optical orthogonal code (2-D OOC) is a set of utimesv matrices with (0, 1) elements having good auto and cross-correlations. Recently, many researchers are working on constructions and designs of 2-D OOCs. In this paper, we shall reveal the combinatorial properties of 2-D OOCs and give an equivalent combinatorial description of a 2-D OOC. Based on this, we are able to use combinatorial methods to obtain many optimal 2-D OOCs.
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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