| Issue |
RAIRO-Theor. Inf. Appl.
Volume 45, Number 2, April-June 2011
|
|
|---|---|---|
| Page(s) | 225 - 234 | |
| DOI | https://doi.org/10.1051/ita/2011018 | |
| Published online | 13 May 2011 | |
Unique decipherability in the additive monoid of sets of numbers
Department of Mathematics
and Turku Centre for Computer Science TUCS,
University of Turku, 20014 Turku, Finland;
amsaar@utu.fi
Received:
22
December
2009
Accepted:
2
February
2011
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 
and
. 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.
Mathematics Subject Classification: 68R05 / 68Q45
Key words: Unique decipherability / rational set / sumset
© EDP Sciences, 2011
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