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On the order of recursive differentiability of finite binary quasigroups
Authors: Parascovia Syrbu
Keywords: quasigroup, recursive derivative, recursively differentiable quasigroup
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Keywords: quasigroup, recursive derivative, recursively differentiable quasigroup
Abstract
The recursive derivatives of an algebraic operation are defined in \cite{CousGonzMarkNech98}, where they appear as control mappings of complete recursive codes. It is proved in \cite{CousGonzMarkNech98}, in particular, that the recursive derivatives of order up to $r$ of a finite binary quasigroup $(Q,\cdot )$ are quasigroup operations if and only if $(Q,\cdot )$ defines a recursive MDS-code of length $r+3$. The author of the present note gives an algebraic proof of an equivalent statement: a finite binary quasigroup $(Q,\cdot )$ is recursively $r$-differentiable $(r\geq 0)$ if and only if the system consisting of its recursive derivatives of order up to $r$ and of the binary selectors, is orthogonal. This involves the fact that the maximum order of recursive differentiability of a finite binary quasigroup of order $q$ does not exceed $q-2$.Moldova State University,
Department of Mathematics
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Department of Mathematics
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DOI
https://doi.org/10.56415/basm.y2023.i3.p103Fulltext
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Contents
- On some applications of relative (p,q)-th order for rating the growths of composite entire functions
- Graphs, Disjoint Matchings and Some Inequalities
- Existence of solutions to multi-point boundary value problem of fractional order on the half-line
- Some subsets in bitopological spaces and bioperations continuity associated
- Approximation of fixed points in convex G-metric spaces
- Finite algebras in the design of multivariate cryptography algorithms
- A note on the Kirichenko--Uskorev structure
- Exact solutions to differential equations with different arguments
- On the order of recursive differentiability of finite binary quasigroups
