On LCD, self dual and isodual cyclic codes over finite chain rings

Cristina Fernandez Cordoba*, Amel Benyettou, Aicha Batoul

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review


In this paper, LCD cyclic, self dual and isodual codes over finite chain rings are investigated. It was proven recently that a non-free LCD cyclic code does not exist over finite chain rings. Based on algebraic number theory, we introduce necessary and sufficient conditions for which all free cyclic codes over a finite chain ring are LCD. We have also obtained conditions on the existence of non trivial self dual cyclic codes of any length when the nilpotency index of the maximal ideal of a finite chain ring is even. Further, several constructions of isodual codes are given based on the factorization of the polynomial x n−1 over a finite chain ring.

Original languageEnglish
Article number101993
Number of pages25
JournalFinite Fields and Their Applications
Publication statusPublished - 1 Mar 2022


  • Cyclic codes
  • Finite chain rings
  • Isodual
  • LCD
  • Self dual


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