Locally Repairable Codes Based on Permutation Cubes and Latin Squares
Bibliographic record
Abstract
The importance of Locally Repairable Codes (LRCs) lies on their applications in distributed storage systems (DSSs). There are two approaches to repair multiple failed nodes: the parallel approach, in which a set of failed nodes are simultaneously repaired; and the sequential method, wherein the failed nodes are repaired successively by making use of known nodes, including those already repaired. LRCs in the joint sequential-parallel mode were investigated with the aim of reducing the repair time in the sequential mode, and in this study, we continue the investigation by providing LRCs with higher repair tolerance. We propose a construction of generator matrices for binary LRCs based on back-circulant Latin squares and$t$-dimensional permutation cubes. The codes based on back-circulant Latin squares have locality$r=5$and availability$t \geq 4 $in the parallel mode and, in the case where$t+1$is neither even nor a multiple of 3, they possess a short block length compared to their counterparts [Tamo and Barg (2014) and Wang and Zhang (2015)]. We present LRCs based on$t$-dimensional permutation$m$-cubes with block length$m^{t}$, locality$r=2m-3$, and availability$t \geq 3$in parallel mode. These codes can repair any set of failed nodes of size up to$2^{t}-1$in the sequential mode in at most$t-1$steps. It is shown that these codes areoverall localwith repair tolerance$2t$in the parallel mode. Finally, we introduce the LRC-AL class of codes, a new class of LRCs which satisfies the property that for any pair of nodes$i,j$, there is a repair set for the failed node$i$that contains the live node$j$.
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 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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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 | 0.002 |
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".