Abstract
Decipherability conditions for codes are investigated by using the approach of Guzmán, who introduced in [7] the notion of variety of codes and established a connection between classes of codes and varieties of monoids. The class of Uniquely Decipherable (UD) codes is a special case of variety of codes, corresponding to the variety of all monoids.
It is well known that the Kraft inequality is a necessary condition for UD codes, but it is not sufficient, in the sense that there exist codes that are not UD and that satisfy the Kraft inequality. The main result of the present paper states that, given a variety \(\mathcal{V}\) of codes, if all the elements of \(\mathcal{V}\) satisfy the Kraft inequality, then \(\mathcal{V}\) is the variety of UD codes. Thus, in terms of varieties, Kraft inequality characterizes UD codes.
Partially supported by Italian MURST Project of National Relevance “Linguaggi Formali e Automi: Metodi, Modelli e Applicazioni”.
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© 2005 Springer-Verlag Berlin Heidelberg
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Burderi, F., Restivo, A. (2005). Varieties of Codes and Kraft Inequality. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_45
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DOI: https://doi.org/10.1007/978-3-540-31856-9_45
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