Bibliographic record
Abstract
An (N, K) codebook is a set of N unit-norm code vectors in a K-dimensional vector space. For its applications, it is desired that the maximum magnitude of inner products between a pair of distinct code vectors should be as small as possible, meeting the Welch bound equality strictly or asymptotically. In this paper, an (N, K) codebook is constructed from a K × N partial matrix with K <; N, where each code vector is equivalent to a column of the matrix. To obtain the K × N matrix, K rows are selected from a J × N matrix Φ, associated with a binary sequence of length J and Hamming weight K, where a set of the selected row indices is equivalent to the index set of nonzero entries of the binary sequence. It is then discovered that the maximum magnitude of inner products between a pair of distinct code vectors is determined by the maximum magnitude of Φ-transform of the binary sequence. Thus, constructing a codebook with small magnitude of inner products is equivalent to finding a binary sequence where the maximum magnitude of its Φ-transform is as small as possible. From the discovery, new classes of codebooks with nontrivial bounds on the maximum inner products are constructed from Fourier and Hadamard matrices associated with binary sequences.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| 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".