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A family of constacyclic codes over F 2 + uF 2 + vF 2 + uvF 2

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Abstract

This paper studies (1 + u)-constacyclic codes over the ring F 2 + uF 2 + vF 2 + uvF 2. It is proved that the image of a (1+u)-constacyclic code of length n over F 2+uF 2+vF 2+uvF 2 under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length 4n. A set of generators of such constacyclic codes for an arbitrary length is determined. Some optimal binary codes are obtained directly from (1 + u)-constacyclic codes over F 2 + uF 2 + vF 2 + uvF 2.

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Authors and Affiliations

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

    Xiaoshan Kai, Shixin Zhu & Liqi Wang

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

    Xiaoshan Kai & Shixin Zhu

Authors
  1. Xiaoshan Kai
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  2. Shixin Zhu
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  3. Liqi Wang
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Corresponding author

Correspondence to Xiaoshan Kai.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 60973125, the Natural Science Foundation of Anhui Province under Grant No. 1208085MA14, and the Fundamental Research Funds for the Central Universities under Grants Nos. 2012HGXJ0040 and 2011HGBZ1298.

This paper was recommended for publication by Editor Lei HU.

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Kai, X., Zhu, S. & Wang, L. A family of constacyclic codes over F 2 + uF 2 + vF 2 + uvF 2 . J Syst Sci Complex 25, 1032–1040 (2012). https://doi.org/10.1007/s11424-012-1001-9

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  • DOI: https://doi.org/10.1007/s11424-012-1001-9

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