IEICE TRANSACTIONS on Fundamentals
Self-Dual Cyclic Codes over Z4[u]/<u2-1> and Their Applications of Z4-Self-Dual Codes Construction
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.10 pp.1724-1729
- Publication Date
- 2018/10/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E101.A.1724
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Yun GAO
Nankai University
Jian GAO
Shandong University of Technology
Fang-Wei FU
Nankai University
Keyword
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Yun GAO , Jian GAO, Fang-Wei FU, "Self-Dual Cyclic Codes over Z4[u]/
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1724/_p
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@ARTICLE{e101-a_10_1724,
author={Yun GAO , Jian GAO, Fang-Wei FU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Self-Dual Cyclic Codes over Z4[u]/
year={2018},
volume={E101-A},
number={10},
pages={1724-1729},
abstract={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.},
keywords={},
doi={10.1587/transfun.E101.A.1724},
ISSN={1745-1337},
month={October},}
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TY - JOUR
TI - Self-Dual Cyclic Codes over Z4[u]/
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1724
EP - 1729
AU - Yun GAO
AU - Jian GAO
AU - Fang-Wei FU
PY - 2018
DO - 10.1587/transfun.E101.A.1724
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2018
AB - 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.
ER -
English
