Ternary $L$-quasigroup string transformations

We construct a word transformation using a finite ternary $L$-quasigroup of order m, which is defined by a set of m multiplication tables of right quasigroups. For a finite ternary $L$-quasigroup, a primality checking algorithm is specified, and for the same $L$-quasigroup with a common left unit, an affinity checking algorithm is specified.