Chinese Quarterly Journal of Mathematics ›› 2014, Vol. 29 ›› Issue (2): 210-214.doi: 10.13371/j.cnki.chin.q.j.m.2014.02.008

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On the Characterization of Cyclic Codes over Ring F2+uF2+vF2

  

  1. School of Mathematics and Physics, Hubei Polytechnic University
  • Received:2012-06-25 Online:2014-06-30 Published:2021-01-25
  • About author:ZHANG Xiao-yan(1979-), female, native of Huangshi, Hubei, an associate professor of Hubei Polytechnic University, engages in algebra coding.
  • Supported by:
    Supported by the Scientific Research Foundation of Education Department of Hubei Province(B2013069); Supported by the National Science Foundation of Hubei Polytechnic University of China(12xjz14A,11yjz37B);

Abstract: In this work, we investigate the cyclic codes over the ring F2+ uF2+ vF2. We first study the relationship between linear codes over F2+ uF2+ vF2 and that over F2.Then we give a characterization of the cyclic codes over F2+ uF2+ vF2 . Finally, we obtain the number of the cyclic code over F2+ uF2+ vF2  of length n. 

Key words: linear code, cyclic code, Gray map, generator matrix

CLC Number: