Acta Mathematica Vietnamica

, Volume 43, Issue 2, pp 357–371 | Cite as

Codes Induced by Alternative Codes

  • Ngo Thi HienEmail author
  • Do Long Van


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.


Code 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.


  1. 1.
    Berstel, J., Perrin, D.: Theory of Codes. Academic Press, New York (1985)zbMATHGoogle Scholar
  2. 2.
    Biegler, F., Daley, M., McQuillan, I.: Algorithmic decomposition of shuffle on words. Theor. Comput. Sci. 454, 38–50 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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
  4. 4.
    Han, Y.S., Salomaa, A., Salomaa, K., Wood, D., Yu, S.: On the existence of prime decompositions. Theor. Comput. Sci. 376, 60–69 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Hien, N.T.: Characterizations for several classes of alternative codes. J. Comput. Sci. Cybern. 32, 273–283 (2016)Google Scholar
  6. 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. 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. 8.
    Jastrzab, T., Czech, Z.J.: A parallel algorithm for the decomposition of finite languages. Stud. Informatica 34, 5–16 (2014)Google Scholar
  9. 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. 10.
    Mollin, R.A.: Fundamental Number Theory with Applications. 2nd edn. Chapman & Hall/CRC, Boca Raton (2008)Google Scholar
  11. 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
  12. 12.
    Schützenberger, M. P.: On a question concerning certain free submonoids. J. Comb. Theory 1, 437–442 (1966)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Shyr, H.J.: Free Monoids and Languages. Hon Min Book Company, Taichung (1991)zbMATHGoogle Scholar
  14. 14.
    Vinh, H.N., Nam, V.T., Huy, P.T.: Codes based on unambiguous products. Lect. Notes Comput. Sci. 6423, 252–262 (2010)CrossRefGoogle Scholar
  15. 15.
    Wieczorek, W.: An algorithm for the decomposition of finite languages. Log. J. IGPL 18, 355–366 (2010)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Hanoi University of Science and TechnologyHanoiVietnam
  2. 2.Institute of Mathematics, Vietnam Academy of Science and TechnologyHanoiVietnam

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