内缀强码的一个刻画

A CHARACTERIZATION OF INFIX STRONG CODES

称码ＣＡ＋为强码，若对任意ｘ，ｙ，ｚ∈Ａ＊，（ｉ）ｘ，ｙｚ∈Ｃ蕴含ｙｘｚ∈Ｃ＋且（ｉ）ｙｘｚ∈Ｃ＋与ｘ∈Ｃ＋蕴含ｙｚ∈Ｃ＊；称码ＣＡ＋为内缀码，若ｘ∈Ｃ且ｙｘｚ∈Ｃ蕴含ｙｚ＝１．本文证明：ＣＡ＋为内缀强码的充要条件是对Ｃ的字母表ＡＣＡ有正整数ｋ，使Ｃ＝ＡｋＣ．此结论是对Ｃ．Ｍ．Ｒｅｉｓ类似结论的补充，亦是Ｈ．Ｊ．

A code CA + is called strong, if for all x,y,z∈A , (i) x,yz∈C imply yxz∈C + and (ii) yxz, x∈C + imply yz∈C ; A code CA + is called infix, if x,yxz∈C imply yz=1 . It is proved in this paper that CA + is an infix strong code if and only if C=A k C for some positive integer k , where A C is the alphabet of C . This result is a complement of similar results due to C. M. Reis and a generalization of the same result on finite strong code due to H. J. shyr.