6533b82efe1ef96bd1293e54
RESEARCH PRODUCT
Monoids and Maximal Codes
Fabio Burderisubject
FOS: Computer and information sciencesDiscrete mathematicsMonoidCode (set theory)Formal Languages and Automata Theory (cs.FL)lcsh:MathematicsComputer Science - Formal Languages and Automata TheoryAstrophysics::Cosmology and Extragalactic Astrophysicslcsh:QA1-939lcsh:QA75.5-76.95Set (abstract data type)chemistry.chemical_compoundchemistryFOS: MathematicsMathematics - CombinatoricsOrder (group theory)High Energy Physics::ExperimentCombinatorics (math.CO)lcsh:Electronic computers. Computer scienceCharacteristic propertyPartially ordered setMaximal elementMathematicsdescription
In recent years codes that are not Uniquely Decipherable (UD) are been studied partitioning them in classes that localize the ambiguities of the code. A natural question is how we can extend the notion of maximality to codes that are not UD. In this paper we give an answer to this question. To do this we introduce a partial order in the set of submonoids of a monoid showing the existence, in this poset, of maximal elements that we call full monoids. Then a set of generators of a full monoid is, by definition, a maximal code. We show how this definition extends, in a natural way, the existing definition concerning UD codes and we find a characteristic property of a monoid generated by a maximal UD code.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-08-17 | Electronic Proceedings in Theoretical Computer Science |