Monoids and Maximal Codes

Details Monoids and Maximal Codes Monoids and Maximal Codes

2011-08-18

arxiv.org/abs/1108.3624v1

EPTCS 63, 2011, pp. 83-92

Computer Science

Formal Languages and Automata Theory

In Proceedings WORDS 2011, arXiv:1108.3412

Scientific paper

10.4204/EPTCS.63.12

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.

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