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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, BoranLee, Yoonjin
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2020
Journal Title
DESIGNS CODES AND CRYPTOGRAPHY
ISSN
0925-1022JCR Link

1573-7586JCR Link
Citation
DESIGNS CODES AND CRYPTOGRAPHY vol. 88, no. 10, pp. 2247 - 2273
Keywords
Self-dual codeCyclic codeChain ringMass formulaGeneratorideal
Publisher
SPRINGER
Indexed
SCIE; SCOPUS WOS 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).
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DOI
10.1007/s10623-020-00776-1
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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