Some Properties Of K-p-infix Codes And Empty Kernel Codes And The Constructions Of The Corresponding Maximal Codes

In 2001, Dongyang Long proved that the p-infix code is closed under product, a (k+1)-p-infix code must be a k-p-infix code, and 2-k-ps-infix code is not closed under product. We study the closures properties of k-p-infix code under the other opera-tions and the sufficient conditions of the closed of 2-k-ps-infix code under product. In addition, the detailed portrait of p-infix code, we mainly study the construction methods of the maximal p-infix code. On the homomorphism which preserves some languages, this paper focus discussion on the homomorphism which preserves the p-infix code and 2-p-infix code. In 2010, the European scholars J.Berstel,C.D.Felice and D.Perrin first proposed the definition of the empty kernel and obtained the nature of the associated with the group codes. In the fourth chapter in this paper, starting from the definition of empty kernel code, we study the basic properties, and sufficient conditions of the closed of empty kernel code under product. We find nec-essary and sufficient condition of depicting the empty kernel languages. Moreover, we also study how to construct the empty kernel code and the method of how to build the maximal empty kernel languages and so on.