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On the structure of cyclic codes over F q + uF q + vF q + uvF q

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Wuhan University Journal of Natural Sciences

Abstract

In this paper, cyclic codes over the ring R = F q + uF q + vF q + uvF q + are discussed where the ring R is not a finite chain ring. By studying the polynomial ring ℜ n = (F q + uF q + vF q + uvF q )[x/(x n − 1) and using the corresponding relationship between the cyclic codes in R and the ideals in ℜ n , cyclic codes over the ring R are characterized. Finally, a Gray-map is obtained and the image of cyclic codes in R is characterized.

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Authors and Affiliations

  1. School of Mathematics and Physics, Huangshi Institute of Technology, Huangshi, 435003, Hubei, China

    Xiaofang Xu & Xiusheng Liu

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  1. Xiaofang Xu
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  2. Xiusheng Liu
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Correspondence to Xiaofang Xu.

Additional information

Foundation item: Supported by the Natural Science Foundation of Hubei Province (B20114410)

Biography: XU Xiaofang, female, Master, Lecturer, research direction: algebra combination and algebra coding.

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Xu, X., Liu, X. On the structure of cyclic codes over F q + uF q + vF q + uvF q . Wuhan Univ. J. Nat. Sci. 16, 457–460 (2011). https://doi.org/10.1007/s11859-011-0780-5

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  • DOI: https://doi.org/10.1007/s11859-011-0780-5

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