New Families of Strength‐3 Covering Arrays Using Linear Feedback Shift Register Sequences
Bibliographic record
Abstract
ABSTRACT In an array over an alphabet of symbols, a ‐set of column indices is covered if each ‐tuple of the alphabet occurs at least once as a row of the sub‐array indexed by . A covering array, denoted by CA, is an array over an alphabet with symbols with the property that any ‐set of columns is covered. Here, is the size and is the strength of the covering array. Raaphorst et al. (Des. Codes Cryptogr. (2014) 73:949‐968) give a construction for a CA, which we denote as , by using linear feedback shift register (LFSR) sequences with characteristic polynomial being a primitive polynomial over . The array corresponds to a covering perfect hash family. We give a construction of covering arrays of strength 3 based on horizontally concatenating copies of , for any prime power and . The coverage is completed by developing Roux‐type constructions that exploit the structure of and remove repeated rows. Some of these covering arrays improve the previous best‐known upper bound of the size of covering arrays with the same corresponding parameters.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".