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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
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2018/10/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Coding Theory
self-dual cyclic codes, gray map, Z4-self-dual codes,
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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.