Existence and nonexistence of permutation trinomials in odd characteristics
Bibliographic record
Abstract
Let Fq be the finite field of order q, where q is a prime power. Very recently, Temür, B. G. and Özkaya, B. [Citation35] investigated the permutation property over Fq2 of the trinomials x3+xq+2−x4q−1 and x4q−1+x2q+1−x3 when characteristic of Fq is 3. In this paper, for odd q and α∈Fq∗ we investigate the permutation property over Fq2 of the trinomials αx3+xq+2−x4q−1, αx3+x2q+1+x4q−1 and x5+αxq+4+x5q. Our results also generalize the work of Akbal, Y., Temür, B. G., and Ongan, P. [Citation1].
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".