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On a complete set of operations for factorizing codes

Published online by Cambridge University Press:  15 October 2005

Clelia De Felice
Clelia De Felice*
Affiliation:
Dipartimento di Informatica e Applicazioni, Università di Salerno, 84081 Baronissi (SA), Italy; defelice@dia.unisa.it
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Abstract

It is known that the class of factorizing codes, i.e., codes satisfying the factorization conjecture formulated by Schützenberger, is closed under two operations: the classical composition of codes and substitution of codes. A natural question which arises is whether a finite set O of operations exists such that each factorizing code can be obtained by using the operations in O and starting with prefix or suffix codes. O is named here a complete set of operations (for factorizing codes). We show that composition and substitution are not enough in order to obtain a complete set. Indeed, we exhibit a factorizing code over a two-letter alphabet A = {a,b}, precisely a 3-code, which cannot be obtained by decomposition or substitution.

Keywords

Variable length codesformal languagesfactorizations of cyclic groups.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 1 , January 2006 , pp. 29 - 52
Copyright
© EDP Sciences, 2006

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