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On the Gray images of some constacyclic codes over F p + u F p + u 2 F p

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Abstract

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, a new Gray map between codes over F p + u F p + u 2 F p and codes over F p is defined, where p is an odd prime. By means of this map, it is shown that the Gray image of a linear (1+u+u 2)-constacyclic code over F p + u F p + u 2 F p of length n is a repeated-root cyclic code over F p of length pn. Furthermore, some examples of optimal linear cyclic codes over F 3 from (1 + u + u 2)-constacyclic codes over F 3 + u F 3 + u 2 F 3 are given.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Hefei University, Hefei, 230601, China

    Haifeng Yu

  2. School of Mathematics, Hefei University of Technology, Hefei, 230009, China

    Shixin Zhu & Xiaoshan Kai

  3. National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, China

    Shixin Zhu & Xiaoshan Kai

Authors
  1. Haifeng Yu
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  2. Shixin Zhu
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  3. Xiaoshan Kai
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Corresponding author

Correspondence to Haifeng Yu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61370089, the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University under Grant No. 2014D04, the Natural Science Fund of Education Department of Anhui province under Grant No. KJ2013Z276, the Fundamental Research Funds of Hefei University under Grant No. 10KY01ZD, the Key construction discipline Funds of Hefei University under Grant No. 2014XK08, and the Natural Science Key Fund of Education Department of Anhui Province under Grant No. KJ2015A226.

This paper was recommended for publication by Editor DENG Yingpu.

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Yu, H., Zhu, S. & Kai, X. On the Gray images of some constacyclic codes over F p + u F p + u 2 F p . J Syst Sci Complex 29, 842–849 (2016). https://doi.org/10.1007/s11424-015-4316-5

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  • DOI: https://doi.org/10.1007/s11424-015-4316-5

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