|
Short communications
On the order of recursive differentiability of finite binary quasigroups
Parascovia Syrbu Moldova State University, Department of Mathematics
Abstract:
The recursive derivatives of an algebraic operation are defined in [1], where they appear as control mappings of complete recursive codes. It is proved in [1], 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 $q-2$.
Keywords and phrases:
quasigroup, recursive derivative, recursively differentiable quasigroup.
Received: 21.07.2021
Citation:
Parascovia Syrbu, “On the order of recursive differentiability of finite binary quasigroups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2023, no. 3, 103–106
Linking options:
https://www.mathnet.ru/eng/basm606 https://www.mathnet.ru/eng/basm/y2023/i3/p103
|
Statistics & downloads: |
Abstract page: | 45 | Full-text PDF : | 15 | References: | 6 |
|