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The Relation Between k-Circularity and Circularity of Codes
Elena Fimmel1, Christian J Michel2, François Pirot3,4
1Institute of Mathematical Biology, Faculty for Computer Sciences, Mannheim University of Applied Sciences, 68163, Mannheim, Germany.
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 [Formula: see text], an integer k such that every k-circular [Formula: see text]-letter code over an alphabet of cardinality n is circular, and we determine the least such integer k for all values of n and [Formula: see text]. 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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