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Some Results on \({(\varvec{k,m})}\)-Comma Codes

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Abstract

Suppose that L is a nonempty language over A, \(k\in \mathbb {N}^0\) and \(m\in \mathbb {N}\). If L satisfies \((LA^k)^mL\)\(\cap A^+(LA^k)^{m-1}LA^+=\emptyset \), then L is a code and is called a (km)-comma code. If L is a (km)-comma code, then it is known that L is an infix code when \(m=1\) and L is a bifix code when \(m\ge 1\). In this paper, we extend the study and find that the class of (km)-comma codes and the class of infix codes are incomparable but they are not disjoint, so we first characterize the (km)-comma codes with \(m\ge 2\) which are infix codes. We also describe the solid codes with minimum lengths greater than k and the 2-(k, 1)-comma codes by different approaches. Finally, the class of bifix codes will be classified into disjoint union of some subclasses and a criterion to determine the subclass membership of a given bifix code will be given.

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Acknowledgements

The authors would like to thank the referees for their reading the manuscript carefully and for providing some valuable revising suggestions.

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Correspondence to Yuqi Guo.

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Communicated by Hamid Reza Ebrahimi Vishki.

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This work is supported by National Natural Science Foundation of China #11861051.

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Liu, H., Shum, K.P. & Guo, Y. Some Results on \({(\varvec{k,m})}\)-Comma Codes. Bull. Iran. Math. Soc. 46, 1143–1162 (2020). https://doi.org/10.1007/s41980-019-00318-z

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  • DOI: https://doi.org/10.1007/s41980-019-00318-z

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