# Finite completion of comma-free codes. Part 1

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2004)

- Volume: 38, Issue: 2, page 91-115
- ISSN: 0988-3754

## Access Full Article

top## Abstract

top## How to cite

topLam, Nguyen Huong. "Finite completion of comma-free codes. Part 1." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 38.2 (2004): 91-115. <http://eudml.org/doc/245677>.

@article{Lam2004,

abstract = {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.},

author = {Lam, Nguyen Huong},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {comma-free code; completion; finite maximal comma-free code},

language = {eng},

number = {2},

pages = {91-115},

publisher = {EDP-Sciences},

title = {Finite completion of comma-free codes. Part 1},

url = {http://eudml.org/doc/245677},

volume = {38},

year = {2004},

}

TY - JOUR

AU - Lam, Nguyen Huong

TI - Finite completion of comma-free codes. Part 1

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 2

SP - 91

EP - 115

AB - 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.

LA - eng

KW - comma-free code; completion; finite maximal comma-free code

UR - http://eudml.org/doc/245677

ER -

## References

top- [1] J. Berstel and D. Perrin, Theory of Codes. Academic Press, Orlando (1985). Zbl0587.68066MR797069
- [2] F.H.C. Crick, J.S. Griffith and L.E. Orgel, Codes without Commas. Proc. Natl. Acad. Sci. USA 43 (1957) 416-421. MR86734
- [3] S.W. Golomb, B. Gordon and L.R. Welch, Comma-free Codes. Canad. J. Math. 10 (1958) 202-209. Zbl0081.14601MR95091
- [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. Zbl0138.15102MR188006
- [6] C.M. Fan and H.J. Shyr, Some Properties of Maximal Comma-free Codes. Tamkang J. Math. 29 (1998) 121-135. Zbl0978.68088MR1644395
- [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. Zbl0794.68087MR1135474
- [8] B.H. Jiggs, Recent Results in Comma-free Codes. Canad. J. Math. 15 (1963) 178-187. Zbl0108.14304MR143672
- [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.
- [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. Zbl0154.00703MR210594
- [11] A. Restivo, On Codes Having No Finite Completions. Discret Math. 17 (1977) 306-316. Zbl0357.94011MR498922
- [12] R.A. Scholtz, Maximal and Variable Word-length Comma-free Codes. IEEE Trans. Inform. Theory IT-15 (1969) 555-559. Zbl0172.43104MR250754
- [13] H.J. Shyr, Free Monoids and Languages. Lecture Notes, Hon Min Book Company, Taichung (1991). Zbl0746.20050MR1090325
- [14] J.D. Watson and F.C.H. Crick, A Structure for Deoxyribose Nucleic Acid. Nature 171 (1953) 737.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.