A comparison of evolutionary algorithms for finding optimal error-correcting codes
Why this work is in the frame
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Bibliographic record
Abstract
The maximum possible number of codewords in a q-ary code of length n and minimum distance d is denoted Aq(n, d). It is a fundamental problem in coding theory to determine this value for given parameters q, n and d. Codes that attain the maximum are said to be optimal. Unfortunately, for many different values of these parameters, the maximum number of codewords is currently unknown: instead we have a known upper bound and a known lower bound for this value. In this paper, we investigate the use of different evolutionary algorithms for improving lower bounds for given parameters. We relate this problem to the well-known Maximum Clique Problem. We compare the performance of the evolutionary algorithms to Hill Climbing, Beam Search, Simulated Annealing, and greedy methods. We found that the GAs outperformed all other algorithms in general; furthermore, the difference in performance became more significant when considering harder test cases.
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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) | 0.000 | 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 | 0.001 | 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 it