UNIQUE DECIPHERABILITY IN THE ADDITIVE MONOID OF SETS OF NUMBERS

: Saarela A

Publisher: CAMBRIDGE UNIV PRESS

: 2011

: RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications

: RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS

: RAIRO-THEOR INF APPL

: 2

: 45

: 2

: 225

: 234

: 10

: 0988-3754

DOI: https://doi.org/10.1051/ita/2011018

Sets of integers form a monoid, where the product of two sets A and B is defined as the set containing a vertical bar b for all a is an element of A and b is an element of B. We give a characterization of when a family of finite sets is a code in this monoid, that is when the sets do not satisfy any nontrivial relation. We also extend this result for some infinite sets, including all infinite rational sets.