Coding Partitions: Regularity, Maximality and Global Ambiguity

  • Marie-Pierre Béal
  • Fabio Burderi
  • Antonio Restivo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4588)

Abstract

The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite sequences.

We firstly prove that the canonical coding partition of a regular set contains a finite number of regular classes. We give an algorithm for computing this partition. We then investigate maximality conditions in a coding partition and we prove, in the regular case, the equivalence between two different notions of maximality. As an application, we finally derive some new properties of maximal uniquely decipherable codes.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Marie-Pierre Béal
    • 1
  • Fabio Burderi
    • 2
  • Antonio Restivo
    • 2
  1. 1.Institut Gaspard-Monge, Laboratoire d’informatique UMR 8049, Université de Marne-la-Vallée, 77454 Marne-la-Vallée Cedex 2France
  2. 2.Dipartimento di Matematica ed Applicazioni, Università degli studi di Palermo, Via Archirafi 34, 90123 PalermoItaly

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