Application of ternary quasigroups to string transformation

We construct a word transformation algorithm using a finite ternary quasigroup, which is defined by a three-dimensional matrix of a special kind. A sufficient sign of simplicity and a sign of polynomial completeness of a finite ternary quasigroup are proved. A method has been developed to verify the polynomial completeness property of a finite ternary quasigroup by considering its corresponding three-dimensional matrix.