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The Gray image of a class of constacyclic codes over the ring Fpm[u]/

  • Department of Common Courses, Anhui Xinhua University, Hefei 230088, China

Cite this: JUSTC, 2017, 47(7): 610-620
https://doi.org/10.3969/j.issn.0253-2778.2017.07.009
Funds: Supported by National Natural Science Foundation of China(61370089), Anhui Province Natural Science Research (KJ2015A308, KJ2016A307, KJ2017A623) and Anhui Province Colleges Outstanding Young Talents Program (gxyqZD2016389).
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  • Author Bio:

    DING Jian, male, born in 1982, Master/Associate Professor. Research field: Algebraic coding. E-mail: dingjian_happy@163.com.

  • Corresponding author:

    LI Hongju

  • Received Date: October 26, 2015
  • Revised Date: May 23, 2016
  • Published Date: July 30, 2017
    Abstract
  • Let R(pm,k)=Fpm［u］/, where pj－1+1≤k≤pj and uk=0 for some positive prime number p and positive integer j. A new Gray map from R(pm,k) to Fpmpj was defined. It was proved that the Gray image of a linear (1+u+…+uk－1) constacyclic code of an arbitrary length N over R(pm,k) is a distance invariant linear cyclic code of length pjN over Fpm. Moreover, the generator polynomial of the Gray image of such a constacyclic code was determined, and some optimal linear cyclic codes over F3, F5 and F7 were constructed via the Gray map.
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