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Classification of self-dual cyclic codes over the chain ring Z(p)[u]/< u(3)>
- Title
- Classification of self-dual cyclic codes over the chain ring Z(p)[u]/< u(3)>
- Authors
- Kim, Boran; Lee, Yoonjin
- Ewha Authors
- 이윤진
- SCOPUS Author ID
- 이윤진
- Issue Date
- 2020
- Journal Title
- DESIGNS CODES AND CRYPTOGRAPHY
- ISSN
- 0925-1022
1573-7586
- Citation
- DESIGNS CODES AND CRYPTOGRAPHY vol. 88, no. 10, pp. 2247 - 2273
- Keywords
- Self-dual code; Cyclic code; Chain ring; Mass formula; Generator; ideal
- Publisher
- SPRINGER
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- We classify all the cyclic self-dual codes of length p(k) over the finite chain ring R := Z(p)[u]/< u(3)>, 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 p(k) for every prime p. We then prove that if a cyclic code over R of length p(k) is self-dual, then p should be equal to 2. Furthermore, we completely determine the generators of all the cyclic self-dual codes over Z(p)[u]/< u(3)> of length 2(k). Finally, we obtain a mass formula for counting cyclic self-dual codes over Z(p)[u]/< u(3)> of length 2(k).
- DOI
- 10.1007/s10623-020-00776-1
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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