Codes Induced by Alternative Codes
- 41 Downloads
Alternative codes, an extension of the notion of ordinary codes, have been first introduced and considered by Huy and Nam (2004). As seen below, every alternative code, in its turn, defines an ordinary code. Such codes are called codes induced by alternative codes or alt-induced codes, for short. In this paper, we consider these alt-induced codes and subclasses of them. In particular, characteristic properties of such codes are established, and an algorithm to check whether a finite code is alt-induced or not is proposed.
KeywordsCode Alt-induced code Strong alt-induced code Alternative code Strong alternative code
Mathematics Subject Classification (2010)94A45 68Q45
The authors would like to thank the colleagues in the Seminar on Mathematical Foundation of Computer Science at Institute of Mathematics, Vietnam Academy of Science and Technology for attention to this work. Especially, the authors express their sincere thanks to Dr. Nguyen Huong Lam and Dr. Kieu Van Hung for their useful discussions.
- 3.Han, N.D., Huy, P.T.: On unambiguity of languages related to codes. In: James, J.P., Victor, C.M.L., Cho, L.W., Taeshik, S. (eds.) Future Information Technology, Application, and Service, pp 32–38. Springer, Netherlands (2012)Google Scholar
- 5.Hien, N.T.: Characterizations for several classes of alternative codes. J. Comput. Sci. Cybern. 32, 273–283 (2016)Google Scholar
- 6.Hung, K.V., Van, D.L.: Prime decomposition problem for several kinds of regular codes. Lec. Notes Comput. Sci. 4281, 213–227 (2006)Google Scholar
- 7.Huy, P.T., Nam, V.T.: Alternative codes and pre-context codes. The 7th National conference: Selected problems about IT and Telecommunication, pp. 188–197. (in Vietnamese) (2004)Google Scholar
- 8.Jastrzab, T., Czech, Z.J.: A parallel algorithm for the decomposition of finite languages. Stud. Informatica 34, 5–16 (2014)Google Scholar
- 9.Jürgensen, H., Konstantinidis, S.: Codes. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, pp 511–607. Springer, Berlin (1997)Google Scholar
- 10.Mollin, R.A.: Fundamental Number Theory with Applications. 2nd edn. Chapman & Hall/CRC, Boca Raton (2008)Google Scholar
- 11.Sardinas, A.A., Patterson, C.W.: A necessary and sufficient condition for the unique decomposition of coded messages. IRE Int. Conv. Rec. 8, 104–108 (1953)Google Scholar