A Simple Deterministic Reduction for the Gap Minimum Distance of Code\n Problem
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Bibliographic record
Abstract
We present a simple deterministic gap-preserving reduction from SAT to the\nMinimum Distance of Code Problem over $\\F_2$. We also show how to extend the\nreduction to work over any finite field. Previously a randomized reduction was\nknown due to Dumer, Micciancio, and Sudan, which was recently derandomized by\nCheng and Wan. These reductions rely on highly non-trivial coding theoretic\nconstructions whereas our reduction is elementary.\n As an additional feature, our reduction gives a constant factor hardness even\nfor asymptotically good codes, i.e., having constant rate and relative\ndistance. Previously it was not known how to achieve deterministic reductions\nfor such codes.\n
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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 it