Bounds on r-identifying codes in q-ary Lee space
Bibliographic record
Abstract
Identifying codes are used to locate malfunctioning processors in multiprocessor systems. In this paper, we study identifying codes in a $q$-ary hypercube which is used in parallel processing. Computing upper and lower bounds of $M_{r,q}(n),$ the smallest cardinality among all $r$-identifying codes in $\mathbb{Z}_q^n$ with respect to the Lee metric, is an important research problem in this area. Using our constructions, we produce tables for upper and lower bounds for $M_{r,q}(n)$. The upper and the lower bounds of $M_{r,4}(n)$ known only when $r=1$ but using our results, we compute the bounds for $M_{r,4}(n)$ for all $r\geq 1$. Also we improve upon the currently known upper bounds of $M_{1,4}(n)$ due to J. L. Kim and S. J. Kim. Upper bounds of $M_{r,q}(n)$ for $q>4$ are known previously for some cases of $n$. We improve some of these bounds and we also compute bounds for all $n$ by using our results.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 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 | 0.000 |
| 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".