On the Construction and Dimensionality of Linear Block Code Trellises
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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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 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".