A hierarchy for circular codes

Giuseppe Pirillo

RAIRO - Theoretical Informatics and Applications (2008)

  • Volume: 42, Issue: 4, page 717-728
  • ISSN: 0988-3754

Abstract

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We first prove an extremal property of the infinite Fibonacci* word f: the family of the palindromic prefixes {hn | n ≥ 6} of f is not only a circular code but “almost” a comma-free one (see Prop. 12 in Sect. 4). We also extend to a more general situation the notion of a necklace introduced for the study of trinucleotides codes on the genetic alphabet, and we present a hierarchy relating two important classes of codes, the comma-free codes and the circular ones.

How to cite

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Pirillo, Giuseppe. "A hierarchy for circular codes." RAIRO - Theoretical Informatics and Applications 42.4 (2008): 717-728. <http://eudml.org/doc/250358>.

@article{Pirillo2008,
abstract = { We first prove an extremal property of the infinite Fibonacci* word f: the family of the palindromic prefixes \{hn | n ≥ 6\} of f is not only a circular code but “almost” a comma-free one (see Prop. 12 in Sect. 4). We also extend to a more general situation the notion of a necklace introduced for the study of trinucleotides codes on the genetic alphabet, and we present a hierarchy relating two important classes of codes, the comma-free codes and the circular ones. },
author = {Pirillo, Giuseppe},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Theory of codes; comma-free codes; circular codes.; theory of codes; circular codes},
language = {eng},
month = {1},
number = {4},
pages = {717-728},
publisher = {EDP Sciences},
title = {A hierarchy for circular codes},
url = {http://eudml.org/doc/250358},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Pirillo, Giuseppe
TI - A hierarchy for circular codes
JO - RAIRO - Theoretical Informatics and Applications
DA - 2008/1//
PB - EDP Sciences
VL - 42
IS - 4
SP - 717
EP - 728
AB - We first prove an extremal property of the infinite Fibonacci* word f: the family of the palindromic prefixes {hn | n ≥ 6} of f is not only a circular code but “almost” a comma-free one (see Prop. 12 in Sect. 4). We also extend to a more general situation the notion of a necklace introduced for the study of trinucleotides codes on the genetic alphabet, and we present a hierarchy relating two important classes of codes, the comma-free codes and the circular ones.
LA - eng
KW - Theory of codes; comma-free codes; circular codes.; theory of codes; circular codes
UR - http://eudml.org/doc/250358
ER -

References

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  15. C.J. Michel, G. Pirillo and M.A. Pirillo, Varieties of comma-free codes. Comput. Math. Appl. (in press).  
  16. F. Mignosi and G. Pirillo, Repetitions in the Fibonacci infinite word. RAIRO-Theor. Inf. Appl.26 (1992) 199–204.  
  17. G. Pirillo, Infinite words and biprefix codes. Inform. Process Lett.50 293–295 (1994).  
  18. G. Pirillo, Fibonacci numbers and words. Discrete Math.173 (1997) 197–207.  
  19. G. Pirillo, Some factorizations of the Fibonacci word. Algebra Colloquium6 (1999) 361–368.  
  20. G. Pirillo, A characterization for a set of trinucleotides to be a circular code, In Determinism, Holism, and Complexity, edited by C. Pellegrini, P. Cerrai, P. Freguglia, V. Benci and G. Israel. Kluwer (2003).  
  21. G. Pirillo and M.A. Pirillo, Growth function of self-complementary circular codes. Biology Forum98 (2005) 97–110.  
  22. P.P. Séébold, Propriétés combinatoires des mots infinis engendrés par certains morphismes. PhD. thesis, L.I.T.P., Paris. (1985).  

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