no. 2
Finite completion of comma-free codes. Part 1
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 2, pp. 91-115

This paper is the first step in the solution of the problem of finite completion of comma-free codes. We show that every finite comma-free code is included in a finite comma-free code of particular kind, which we called, for lack of a better term, canonical comma-free code. Certainly, finite maximal comma-free codes are always canonical. The final step of the solution which consists in proving further that every canonical comma-free code is completed to a finite maximal comma-free code, is intended to be published in a forthcoming paper.

DOI : 10.1051/ita:2004006
Classification : 68R15, 68S05
Keywords: comma-free code, completion, finite maximal comma-free code 
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     title = {Finite completion of comma-free codes. {Part} 1},
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Lam, Nguyen Huong. Finite completion of comma-free codes. Part 1. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 2, pp. 91-115. doi: 10.1051/ita:2004006

[1] J. Berstel and D. Perrin, Theory of Codes. Academic Press, Orlando (1985). | Zbl | MR

[2] F.H.C. Crick, J.S. Griffith and L.E. Orgel, Codes without Commas. Proc. Natl. Acad. Sci. USA 43 (1957) 416-421. | MR

[3] S.W. Golomb, B. Gordon and L.R. Welch, Comma-free Codes. Canad. J. Math. 10 (1958) 202-209. | Zbl | MR

[4] S.W. Golomb, L.R. Welch and M. Delbrück, Construction and Properties of Comma-free Codes. Biol. Medd. Dan. Vid. Selsk 23 (1958) 3-34.

[5] W.L. Eastman, On the Construction of Comma-free Codes. IEEE Trans. Inform. Theory IT-11 (1965) 263-267. | Zbl | MR

[6] C.M. Fan and H.J. Shyr, Some Properties of Maximal Comma-free Codes. Tamkang J. Math. 29 (1998) 121-135. | Zbl | MR

[7] M. Ito, H. Jürgensen, H.J. Shyr and G. Thierrin, Outfix and Infix Codes and Related Classes of Languages. J. Comput. Syst. Sci. 43 (1991) 484-508. | Zbl | MR

[8] B.H. Jiggs, Recent Results in Comma-free Codes. Canad. J. Math. 15 (1963) 178-187. | Zbl | MR

[9] N.H. Lam, Finite Completion of Comma-free Codes. Part I, in Proc. DLT. Springer-Verlag, Lect. Notes Comput. Sci. 2450 (2002) 357-368. | Zbl

[10] Al. A. Markov, An Example of an Idependent System of Words Which Cannot Be Included in a Finite Complete System. Mat. Zametki 1 (1967) 87-90. | Zbl | MR

[11] A. Restivo, On Codes Having No Finite Completions. Discret Math. 17 (1977) 306-316. | Zbl | MR

[12] R.A. Scholtz, Maximal and Variable Word-length Comma-free Codes. IEEE Trans. Inform. Theory IT-15 (1969) 555-559. | Zbl | MR

[13] H.J. Shyr, Free Monoids and Languages. Lecture Notes, Hon Min Book Company, Taichung (1991). | Zbl | MR

[14] J.D. Watson and F.C.H. Crick, A Structure for Deoxyribose Nucleic Acid. Nature 171 (1953) 737.

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