Self-Dual Cyclic Codes over Z4[u]/<u2-1> and Their Applications of Z4-Self-Dual Codes Construction

Yun GAO   Jian GAO  Fang-Wei FU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.10   pp.1724-1729
Publication Date: 2018/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.1724
Type of Manuscript: LETTER
Category: Coding Theory
Keyword: 
self-dual cyclic codes,  gray map,  Z4-self-dual codes,  

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Summary: 
In this paper, we study self-dual cyclic codes of length n over the ring R=Z4[u]/<u2-1>, where n is an odd positive integer. We define a new Gray map φ from R to Z42. It is a bijective map and maintains the self-duality. Furthermore, we give the structures of the generators of cyclic codes and self-dual cyclic codes of odd length n over the ring R. As an application, some self-dual codes of length 2n over Z4 are obtained.