On the Syntactic Monoids Associated with a Class of Synchronized Codes

A complete code over an alphabet is called synchronized if there exist such that . In this paper we describe the syntactic monoid of for a complete synchronized code over such that , the semigroup generated by , is a single class of its syntactic congruence . In particular, we prove that, for such a code , either or is isomorphic to a special submonoid of , where and are the full transformation semigroups on the nonempty sets and , respectively.