Bibliographic record
Abstract
The most computationally intensive step of the Guruswami-Sudan list decoder for generalized Reed-Solomon codes is the formation of a bivariate interpolation polynomial. Complexity can be reduced if this polynomial has prefactors, i.e., factors of its univariate constituent polynomials that are independent of the received vector, and hence known a priori. For example, the well-known re-encoding projection due to Koetter et al. leads to one class of prefactors. This paper introduces so-called Sierpínski prefactors that result from the property that many binomial coefficients, which arise in the multiplicity constraints defined in terms of the Hasse derivative, are zero modulo the underlying field characteristic. It is shown that re-encoding prefactors and Sierpínski prefactors can be combined to achieve a significantly reduced Guruswami-Sudan interpolation step. In certain practically relevant cases, the introduction of Sierpínski prefactors reduces the number of unknown polynomial coefficients by an additional 10% or more (beyond the reduction due to re-encoding prefactors alone), without incurring additional computational effort at the decoder.
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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 | 0.002 |
| 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 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".