Some Results on the Existence of $t$ -All-or-Nothing Transforms Over Arbitrary Alphabets
Bibliographic record
Abstract
A (t, s, v)-all-or-nothing transform (AONT) is a bijective mapping defined on s-tuples over an alphabet of size v, which satisfies the condition that the values of any t input co-ordinates are completely undetermined, given only the values of any s - t output co-ordinates. The main question we address in this paper is: for which choices of parameters does a (t, s, v)-AONT exist? More specifically, if we fix t and v, we want to determine the maximum integer s such that a (t, s, v)-AONT exists. We mainly concentrate on the case t = 2 for arbitrary values of v, where we obtain various necessary as well as sufficient conditions for existence of these objects. This includes computer searches that establish the existence of (2, q, q)-AONT for all odd primes not exceeding 29. We also show some connections between AONT, orthogonal arrays, and resilient functions.
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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 | 0.001 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".