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Negacyclic self-dual codes over finite chain rings

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Abstract

In this article, we study negacyclic self-dual codes of length n over a finite chain ring R when the characteristic p of the residue field \({\bar{R}}\) and the length n are relatively prime. We give necessary and sufficient conditions for the existence of (nontrivial) negacyclic self-dual codes over a finite chain ring. As an application, we construct negacyclic MDR self-dual codes over GR(p t, m) of length p m + 1.

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230009, Anhui, People’s Republic of China

    Xiaoshan Kai & Shixin Zhu

  2. National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, People’s Republic of China

    Xiaoshan Kai & Shixin Zhu

Authors
  1. Xiaoshan Kai
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  2. Shixin Zhu
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Correspondence to Xiaoshan Kai.

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Communicated by J. Wolfmann.

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Kai, X., Zhu, S. Negacyclic self-dual codes over finite chain rings. Des. Codes Cryptogr. 62, 161–174 (2012). https://doi.org/10.1007/s10623-011-9500-6

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  • DOI: https://doi.org/10.1007/s10623-011-9500-6

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