The relation between k-circularity and circularity of codes

Abstract : A code X is k-circular if any concatenation of at most k words from X, when read on a circle, admits exactly one partition into words from X. It is circular if it is k-circular for every integer k. While it is not a priori clear from the definition, there exists, for every pair (n,ℓ), an integer k such that every k-circular ℓ-letter code over an alphabet of cardinality n is circular, and we determine the least such integer k for all values of n and ℓ. The k-circular codes may represent an important evolutionary step between the circular codes, such as the comma-free codes, and the genetic code.
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Submitted on : Tuesday, February 4, 2020 - 4:30:14 PM
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Elena Fimmel, Christian Michel, François Pirot, Jean-Sébastien Sereni, Martin Starman, et al.. The relation between k-circularity and circularity of codes. 2020. ⟨hal-02466859⟩

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