Skew cyclic codes over 𝔽p + u𝔽p
Bibliographic record
Abstract
In this paper, we study skew cyclic codes with arbitrary length over the ring R = 𝔽p + u𝔽p where p is an odd prime and u2 = 0. We characterise all skew cyclic codes of length n as left R[x;θ]-submodules of Rn = R[x;θ] / ⟨xn – 1⟩. We find all generator polynomials for these codes and describe their minimal spanning sets. Moreover, an encoding algorithm is presented for skew cyclic codes over the ring R. Finally, based on the theory we developed in this paper, we provide examples of codes with good parameters over Fp with different odd primes p: In fact, example 6 in our paper is a new ternary code in the class of quasi-twisted codes. We also present several examples of optimal codes.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.003 |
| 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".