IEICE TRANSACTIONS on Fundamentals
On the Gray Image of Cyclic Codes over Finite Chain Rings
Summary :
We introduce (1-γ)-cyclic code and cyclic codes over the finite chain ring R. We prove that the Gray image of a linear (1-γ)-cyclic code over R of length n is a distance invariant quasi-cyclic code over Fpk. We also prove that if (n,p)=1, then every code over Fpk which is the Gray image of a cyclic code over R of length n is equivalent to a quasi-cyclic code.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.9 pp.2685-2687
- Publication Date
- 2008/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e91-a.9.2685
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Keyword
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Jianfa QIAN, Wenping MA, Xinmei WANG, "On the Gray Image of Cyclic Codes over Finite Chain Rings" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 9, pp. 2685-2687, September 2008, doi: 10.1093/ietfec/e91-a.9.2685.
Abstract: We introduce (1-γ)-cyclic code and cyclic codes over the finite chain ring R. We prove that the Gray image of a linear (1-γ)-cyclic code over R of length n is a distance invariant quasi-cyclic code over Fpk. We also prove that if (n,p)=1, then every code over Fpk which is the Gray image of a cyclic code over R of length n is equivalent to a quasi-cyclic code.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.9.2685/_p
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@ARTICLE{e91-a_9_2685,
author={Jianfa QIAN, Wenping MA, Xinmei WANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Gray Image of Cyclic Codes over Finite Chain Rings},
year={2008},
volume={E91-A},
number={9},
pages={2685-2687},
abstract={We introduce (1-γ)-cyclic code and cyclic codes over the finite chain ring R. We prove that the Gray image of a linear (1-γ)-cyclic code over R of length n is a distance invariant quasi-cyclic code over Fpk. We also prove that if (n,p)=1, then every code over Fpk which is the Gray image of a cyclic code over R of length n is equivalent to a quasi-cyclic code.},
keywords={},
doi={10.1093/ietfec/e91-a.9.2685},
ISSN={1745-1337},
month={September},}
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TY - JOUR
TI - On the Gray Image of Cyclic Codes over Finite Chain Rings
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2685
EP - 2687
AU - Jianfa QIAN
AU - Wenping MA
AU - Xinmei WANG
PY - 2008
DO - 10.1093/ietfec/e91-a.9.2685
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2008
AB - We introduce (1-γ)-cyclic code and cyclic codes over the finite chain ring R. We prove that the Gray image of a linear (1-γ)-cyclic code over R of length n is a distance invariant quasi-cyclic code over Fpk. We also prove that if (n,p)=1, then every code over Fpk which is the Gray image of a cyclic code over R of length n is equivalent to a quasi-cyclic code.
ER -
English
