Bibliographic record
Abstract
We study network maximum distance separable (MDS) codes, which are a class of network error-correcting codes whose distance attains the Singleton-type bound. The minimum field size of a network MDS code is of particular interest, since it impacts the computing complexity at the network nodes. Previous constructions of network MDS codes, which are applicable to general single-source multicast networks, require large field sizes. In this paper, for two specific classes of network topologies, we derive upper and lower bounds on the minimum field size of the corresponding network MDS codes and present explicit constructions. The proposed upper bounds significantly improve upon the previous ones and differ from the lower bounds only by a small factor, which is asymptotically no more than 2. Additionally, we extend the concept of linear network error-correction coding from the scalar case to the vector case, and demonstrate a class of networks in which the minimum field size of the vector network MDS code is substantially smaller than that of the scalar case.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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".