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27-04-2020 | Original Paper

Self-dual cyclic codes over \({\mathbb {Z}}_4\) of length 4n

Authors: Yuan Cao, Yonglin Cao, Fang-Wei Fu, Guidong Wang

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 1/2022

Abstract

For any odd positive integer n, we express cyclic codes over \({\mathbb {Z}}_4\) of length 4n in a new way. Based on the expression of each cyclic code \({\mathcal {C}}\), we provide an efficient encoder and determine the type of \({\mathcal {C}}\). In particular, we give an explicit representation and enumeration for all distinct self-dual cyclic codes over \({\mathbb {Z}}_4\) of length 4n and correct a mistake in the paper “Concatenated structure of cyclic codes over \({\mathbb {Z}}_4\) of length 4n” (Cao et al. in Appl Algebra Eng Commun Comput 10:279–302, 2016). In addition, we obtain 50 new self-dual cyclic codes over \({\mathbb {Z}}_4\) of length 28.

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Title: Self-dual cyclic codes over of length 4n
Authors: Yuan Cao
Yonglin Cao
Fang-Wei Fu
Guidong Wang
Publication date: 27-04-2020
Publisher: Springer Berlin Heidelberg
Published in: Applicable Algebra in Engineering, Communication and Computing / Issue 1/2022
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-020-00424-0

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Self-dual cyclic codes over \({\mathbb {Z}}_4\) of length 4n

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Other articles of this Issue 1/2022

A partial characterization of Hilbert quasi-polynomials in the non-standard case

Acknowledgment

On the RLWE/PLWE equivalence for cyclotomic number fields

On Euclidean self-dual codes and isometry codes

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