Construction And Some Closure Properties Of Codes With Finite Deciphering Delay

Codes with finite deciphering delay form a family intermediate between pre-fix codes and general codes.In 2010, the European scholars J.Berstel, D.Perrin and C.Reutenauer in their book "Codes and Automata", given three equivalent char-acterizations of the finite deciphering delay code, Any rational code with finite deciphering delay is contained in a maximal rational code with the same delay, and proved that any two composable codes with finite deciphering delay is closed under composition.Since the existing algebraic properties and the potential research value of codes with finite deciphering delay, this article mainly study the properties of codes with finite deciphering delay from two aspects. On the one hand, about the operation which preserves finite deciphering delay, the paper gives, in the second chapter, the sufficient conditions of catenation and homomorphism respectively preserving codes with finite deciphering delay. On the other hand, about construction of codes with finite deciphering delay, the paper gives in the third chapter, based on the specific language Y, a general constructing method of codes with finite deciphering delay. Finally, since the connection between codes with finite deciphering delay and sequential transducer, the last chapter of this article, from the perspective of sequential transducer proves equivalence relation between composition of codes with finite deciphering delay and composition of sequential transducer.