Involutory-Multiple-Lightweight MDS Matrices based on Cauchy-type Matrices
Bibliographic record
Abstract
One of the best methods for constructing maximum distance separable ( \begin{document}$ \operatorname{MDS} $\end{document} ) matrices is based on making use of Cauchy matrices. In this paper, by using some extensions of Cauchy matrices, we introduce several new forms of \begin{document}$ \operatorname{MDS} $\end{document} matrices over finite fields of characteristic 2. A known extension of a Cauchy matrix, called the Cauchy-like matrix, with application in coding theory was introduced in 1985. One of the main contributions of this paper is to apply Cauchy-like matrices to introduce \begin{document}$ 2n \times 2n $\end{document} involutory \begin{document}$ \operatorname{MDS} $\end{document} matrices in the semi-Hadamard form which is a generalization of the previously known methods. We make use of Cauchy-like matrices to construct multiple \begin{document}$ \operatorname{MDS} $\end{document} matrices which can be used in the Feistel structures. We also introduce a new extension of Cauchy matrices to be referred to as Cauchy-light matrices. The introduced Cauchy-light matrices are applied to construct \begin{document}$ n \times n $\end{document} \begin{document}$ \operatorname{MDS} $\end{document} matrices having at least \begin{document}$ 3n-3 $\end{document} entries equal to the unit element \begin{document}$ 1 $\end{document} ; such a matrix is called a lightweight \begin{document}$ \operatorname{MDS} $\end{document} matrix and can be used in the lightweight cryptography. A simple closed-form expression is given for the determinant of Cauchy-light matrices.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.005 |
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".