Classification of self-dual cyclic codes over the chain ring Zp[ u] / ⟨ u3

Boran Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We classify all the cyclic self-dual codes of length pk over the finite chain ring R: = Zp[ u] / ⟨ u3⟩ , which is not a Galois ring, where p is a prime number and k is a positive integer. First, we find all the dual codes of cyclic codes over R of length pk for every prime p. We then prove that if a cyclic code over R of length pk is self-dual, then p should be equal to 2. Furthermore, we completely determine the generators of all the cyclic self-dual codes over Z2[ u] / ⟨ u3⟩ of length 2 k. Finally, we obtain a mass formula for counting cyclic self-dual codes over Z2[ u] / ⟨ u3⟩ of length 2 k.

Original languageEnglish
Pages (from-to)2247-2273
Number of pages27
JournalDesigns, Codes, and Cryptography
Volume88
Issue number10
DOIs
StatePublished - 1 Oct 2020

Keywords

  • Chain ring
  • Cyclic code
  • Generator
  • Mass formula
  • Self-dual code
  • ideal

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