Geodesic
Construction of medial ternary self-orthogonal quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2022), pp. 41-55

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Algorithms for checking if a medial ternary quasigroup has a set of six triple-wise orthogonal principal parastrophes and a set of six triple-wise strongly orthogonal principal parastrophes are found. It is proved that $n$-ary strongly self-orthogonal linear (including medial) quasigroups do not exist when $n>3$. 
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     author = {Iryna Fryz and Fedir Sokhatsky},
     title = {Construction of medial ternary self-orthogonal quasigroups},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {41--55},
     publisher = {mathdoc},
     number = {3},
     year = {2022},
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Iryna Fryz; Fedir Sokhatsky. Construction of medial ternary self-orthogonal quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2022), pp. 41-55. http://geodesic.mathdoc.fr/item/BASM_2022_3_a4/