Geodesic
Unique decipherability in the additive monoid of sets of numbers
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 2, pp. 225-234

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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∈A and b∈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.

DOI : 10.1051/ita/2011018
Classification : 68R05, 68Q45
Keywords: unique decipherability, rational set, sumset 
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     author = {Saarela, Aleksi},
     title = {Unique decipherability in the additive monoid of sets of numbers},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {225--234},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {2},
     year = {2011},
     doi = {10.1051/ita/2011018},
     mrnumber = {2811655},
     zbl = {1218.68108},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2011018/}
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Saarela, Aleksi. Unique decipherability in the additive monoid of sets of numbers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 2, pp. 225-234. doi: 10.1051/ita/2011018

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