Classification of cyclic codes over a non-Galois chain ring Zp[u]/〈u3

Boran Kim, Yoonjin Lee, Jisoo Doo

Research output: Contribution to journalArticlepeer-review

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Abstract

We explicitly determine generators of cyclic codes over a non-Galois finite chain ring Zp[u]/〈u3〉 of length pk, where p is a prime number and k is a positive integer. We completely classify that there are three types of principal ideals of Zp[u]/〈u3〉 and four types of non-principal ideals of Zp[u]/〈u3〉, which are associated with cyclic codes over Zp[u]/〈u3〉 of length pk. We then obtain a mass formula for cyclic codes over Zp[u]/〈u3〉 of length pk.

Original languageEnglish
Pages (from-to)208-237
Number of pages30
JournalFinite Fields and their Applications
Volume59
DOIs
StatePublished - Sep 2019

Keywords

  • Cyclic code
  • Finite chain ring
  • Mass formula

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