Geodesic
On the order of recursive differentiability of finite binary quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2023), pp. 103-106.

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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,⋅) are quasigroup operations if and only if (Q,⋅) 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,⋅) is recursively r-differentiable (r≥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. 
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Parascovia Syrbu. On the order of recursive differentiability of finite binary quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2023), pp. 103-106. https://geodesic-test.mathdoc.fr/item/BASM_2023_3_a8/

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