On a complete set of operations for factorizing codes
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 1, pp. 29-52.

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.

DOI: 10.1051/ita:2005040
Classification: 94A45,  68Q45,  20K01
Keywords: variable length codes, formal languages, factorizations of cyclic groups
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Felice, Clelia De. On a complete set of operations for factorizing codes. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 1, pp. 29-52. doi : 10.1051/ita:2005040. http://www.numdam.org/articles/10.1051/ita:2005040/

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