Abstract
We associate to a maximal codeX on an alphabetA a dynamical system Ω; our main result proves that the property of unique decipherability implies that the partition of Ω associated to the letters ofA is a Bernoulli partition. Surprisingly it is possible to give two very different proofs of this result: the first one uses probability measures on monoids together with methods from automata theory; the other is based on results of entropy theory.
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Hansel, G., Perrin, D. Codes and Bernoulli partitions. Math. Systems Theory 16, 133–157 (1983). https://doi.org/10.1007/BF01744574
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DOI: https://doi.org/10.1007/BF01744574