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unique decipherability

RAIRO - Theoretical Informatics and Applications (1)

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Unique decipherability in the additive monoid of sets of numbers
Aleksi Saarela
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 45 / Issue 2 / April 2011

Published online by Cambridge University Press:

13 May 2011, pp. 225-234

Print publication:

April 2011
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Sets of integers form a monoid, where the product of two sets A and B is defined as the set containing a+b for all $a\in A$ and $b\in B$. 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.