A note on the factorization conjecture |
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Authors: | Clelia De Felice |
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Affiliation: | 1. Dipartimento di Informatica, Università degli Studi di Salerno, via Giovanni Paolo II, 132, 84084?, Fisciano, SA, Italy
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Abstract: | We give partial results on the factorization conjecture on codes proposed by Schützenberger. We consider a family of finite maximal codes $C$ over the alphabet $A = \{a, b\}$ and we prove that the factorization conjecture holds for these codes. This family contains $(p,4)$ -codes, where a $(p,4)$ -code $C$ is a finite maximal code over $A$ such that each word in $C$ has at most four occurrences of $b$ and $a^p \in C$ , for a prime number $p$ . We also discuss the structure of these codes. The obtained results once again show relations between factorizations of finite maximal codes and factorizations of finite cyclic groups. |
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