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

Boran Kim; Yoonjin Lee; Jisoo Doo

doi:10.1016/j.ffa.2019.06.003

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

Boran Kim, Yoonjin Lee, Jisoo Doo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	208-237
Number of pages	30
Journal	Finite Fields and their Applications
Volume	59
DOIs	https://doi.org/10.1016/j.ffa.2019.06.003
State	Published - Sep 2019

Bibliographical note

Publisher Copyright:
© 2019

Keywords

Cyclic code
Finite chain ring
Mass formula

Access to Document

10.1016/j.ffa.2019.06.003

Cite this

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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.",

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AU - Kim, Boran

AU - Lee, Yoonjin

AU - Doo, Jisoo

PY - 2019/9

Y1 - 2019/9

N2 - 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.

AB - 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.

KW - Cyclic code

KW - Finite chain ring

KW - Mass formula

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