Handbook of formal languages, vol. 1
Journal of the ACM (JACM)
Theory of Codes
Fundamenta Informaticae
On the Reversibility of Parallel Insertion, and Its Relation to Comma Codes
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
On the construction of comma-free codes
IEEE Transactions on Information Theory
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In this paper, we introduce the notion of k-comma codes - a proper generalization of the notion of comma-free codes. For a given positive integer k, a k-comma code is a set L over an alphabet Σ with the property that LΣ kL ∩ Σ +LΣ + = ∅. Informally, in a k-comma code, no codeword can be a subword of the catenation of two other codewords separated by a “comma” of length k. A k-comma code is indeed a code, that is, any sequence of codewords is uniquely decipherable. We extend this notion to that of k-spacer codes, with commas of length less than or equal to a given k. We obtain several basic properties of k-comma codes and their generalizations, k-comma intercodes, and some relationships between the families of k-comma intercodes and other classical families of codes, such as infix codes and bifix codes. Moreover, we introduce the notion of n-k-comma intercodes, and obtain, for each k ≥ 0, several hierarchical relationships among the families of n-k-comma intercodes, as well as a characterization of the family of 1-k-comma intercodes.