A new construction of Massey-Omura parallel multiplier over GF(2/sup m/)
Bibliographic record
Abstract
The Massey-Omura multiplier of GF(2/sup m/) uses a normal basis and its bit parallel version is usually implemented using m identical combinational logic blocks whose inputs are cyclically shifted from one another. In the past, it was shown that, for a class of finite fields defined by irreducible all-one polynomials, the parallel Massey-Omura multiplier had redundancy and a modified architecture of lower circuit complexity was proposed. In this article, it is shown that, not only does this type of multiplier contain redundancy in that special class of finite fields, but it also has redundancy in fields GF(2/sup m/) defined by any irreducible polynomial. By removing the redundancy, we propose a new architecture for the normal basis parallel multiplier, which is applicable to any arbitrary finite field and has significantly lower circuit complexity compared to the original Massey-Omura normal basis parallel multiplier. The proposed multiplier structure is also modular and, hence, suitable for VLSI realization. When applied to fields defined by the irreducible all-one polynomials, the multiplier's circuit complexity matches the best result available in the open literature.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".