On triplanes of order twelve admitting an automorphism of order six and their binary and ternary codes
Bibliographic record
Abstract
In this paper we present the complete classification of triplanes (71, 15, 3) admitting an action of the cyclic automorphism group of order six. Up to isomorphism there are 146 such triplanes and these are all triplanes of order 12 known up to now. Further, we analyze binary and ternary codes spanned by the incidence matrices of triplanes (71, 15, 3) and their residual designs. The constructed binary codes are self- complementary, and the ternary codes are self- orthogonal. In addition, we study ternary self-orthogonal codes constructed from the orbit matrices for Z_3 acting on the 146 symmetric 2-(71, 15, 3) designs. Some of the obtained codes have minimum distance one or two less than the best known codes with the same length and dimension. Finally, we discuss k-geodetic graphs from the symmetric (71, 15, 3) designs and their residual and derived designs.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".