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On the structure of some group codes

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Abstract

In this paper, we study the following problem: Which characteristics does a codeC possess when the syntactic monoidsyn(C *) of the star closureC * ofC is a group? For a codeC, if the syntactic monoidsyn(C *) is a group, then we callC a group code. This definition of a group code is different from the one in [1] (see [1], 46–47). Schützenberger had characterized the structure of finite group codes and had proved thatC is a finite group code if and only ifC is a full uniform code (see [5], [8]). Fork-prefix andk-suffix codes withk≥2,k-infix,k-outfix,p-infix,s-infix, right semaphore codes and left semaphore codes, etc., we obtain similar results. It is proved that the above mentioned codes are group codes if and only if they are uniform codes.

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Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, 510275, Guang zhou, People's Republic of china

    Dongyang Long

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  1. Dongyang Long
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Additional information

Communicated by B. M. Schein

The author would like to thank the referee who helped the author with revising the paper. Thanks are also due to Prof. Boris M. Schein for his valuable suggestions and kind help.

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Long, D. On the structure of some group codes. Semigroup Forum 45, 38–44 (1992). https://doi.org/10.1007/BF03025747

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  • DOI: https://doi.org/10.1007/BF03025747

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