On the Construction and Dimensionality of Linear Block Code Trellises
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Bibliographic record
Abstract
The trellis construction methods of Wolf [1], Massey [2], and Forey [3] for general linear block codes are briefly reviewed. An isomorphism between a. trellis constructed using Massey's method and one constructed using Wolf's method is derived. It is confirmed that Wolf's and Massey's trellis constructions also yield minimal trellises. Two simplified methods for minimal trellis construction ate presented, along with a. method to calculate the trellis dimensions that is art alternative to the methods of [2] and [3]. An improvement is found to a lower bound on the maximum trellis dimension due to Muder [4]. It is shown that when equivalent codes are constructed by permutations of the symbol positions the resulting trellis dimensions are fixed near either end, while in the central portion of the trellis the dimensions vary between an attainable upper bound and a lower bound. From the lower bound on the trellis dimensions in the central portion of the trellis it is seen that only codes (and their duals) that meet a certain condition on their minimum distances can possibly have a trellis with a relatively small number of states.
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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 | 0.000 | 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 | 0.000 | 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