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[02266] Constructing ternary quasigroups possessing properties of parastrophic orthogonality

  • Session Time & Room : 3E (Aug.23, 17:40-19:20) @G601
  • Type : Contributed Talk
  • Abstract : A set of $\ell$ orthogonal $n$-ary operations or hypercubes of order $m$ is equivalent to an $(\ell,m^n,\ell-n+1)$ maximum distance separable or MDS code. Consequently, the problem of constructing MDS codes can be reduced to constructing orthogonal operations. We research constructing a ternary medial quasigroup possessing parastrophic orthogonality property. A necessary and sufficient condition that the quasigroup is self-orthogonal, strongly self-orthogonal or totally parastrophically orthogonal is that each polynomial of a certain set is invertible-valued.
  • Classification : 05B15, 20N05
  • Format : Online Talk on Zoom
  • Author(s) :
    • Fedir Sokhatsky (Vasyl` Stus Donetsk National University)
    • Iryna Fryz (Vasyl` Stus Donetsk National University)