Syntactic congruences of codes
We consider syntactic congruences of some codes. As a main result, for an infix code L, it is proved that the following (i) and (ii) are equivalent and that (iii) implies (i), where P-L is the syntactic congruence of L. (i) L is a P-L2-class. (ii) L-m is a P-Lk-class, for given two integers m and k with 1 less than or equal to m less than or equal to k. (iii)L* is a P-L*-class. Next we show that every (i), (ii) and (iii) holds for a strongly infix code L. Moreover we consider properties of syntactic conguences of a residue W(L) for a strongly outfix code L.
syntactic congruence infix code outfix code prefix code suffix code