Improving Locally Recoverable Codes Through Systematic Construction and Lee Metric Analysis
Bibliographic record
Abstract
Locally recoverable codes (LRCs) play a critical role in distributed storage systems by facilitating efficient data recovery in the event of storage device failures or unavailability. A code C is designated as an $(r, \delta)$-LRC if, for each component i of the codewords, there exists a punctured subcode of C that includes i with a length of at most $r+\delta-1$ and a minimum distance of at least $\delta$. An $(r, \delta)$-LRC with locality r allows for the recovery of any $\delta-1$ nodes by accessing data from r additional nodes within the system. In this paper, we introduce a systematic code with ($r, \delta$) information locality using the Lee metric for the first time, where $\delta \geq 2, r=\frac{p-1}{t}$, and $t \mid(p-1)$. The use of the Lee metric enhances the properties of our code by increasing the minimum distance, thereby enabling it to correct a greater number of errors. We establish a bound on the minimum Lee distance of $(r, \delta)$-LRC Lee codes, demonstrating that this bound exceeds the corresponding limit for $(r, \delta)$-LRCs based on Hamming distance. Furthermore, this bound is shown to be sharp in specific cases, including when $r=k=1, r=k \neq 1$, and $r=1 \neq k$.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.012 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| 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".