Classification of self-dual cyclic codes over the chain ring Zp[ u] / ⟨ u3⟩
- 주제(키워드) Chain ring , Cyclic code , Generator , ideal , Mass formula , Self-dual code
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Springer
- 발행년도 2020
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000174876
- 본문언어 영어
- Published As http://dx.doi.org/10.1007/s10623-020-00776-1
초록/요약
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. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
more