@article{99fe5dc9fba34e369b84a759e33e967c,
title = "Classification of self-dual cyclic codes over the chain ring Zp[ u] / ⟨ u3⟩",
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.",
keywords = "Chain ring, Cyclic code, Generator, Mass formula, Self-dual code, ideal",
author = "Boran Kim and Yoonjin Lee",
note = "Funding Information: The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1I1A1A01060467) and also by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2016R1A5A1008055). Yoonjin Lee is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177) and also by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2017R1A2B2004574) Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2020",
month = oct,
day = "1",
doi = "10.1007/s10623-020-00776-1",
language = "English",
volume = "88",
pages = "2247--2273",
journal = "Designs, Codes, and Cryptography",
issn = "0925-1022",
publisher = "Springer Netherlands",
number = "10",
}