IEICE TRANSACTIONS on Fundamentals
Constacyclic and Cyclic Codes over F2+uF2+u2F2
Summary :
A new Gray map between codes over F2+uF2+u2F2 and codes over F2 is defined. We prove that the Gray image of a linear (1-u2)-cyclic code over F2+uF2+u2F2 of length n is a binary distance invariant linear quasi-cyclic code. We also prove that, if n is odd, then every binary code which is the Gray image of a linear cyclic code over F2+uF2+u2F2 of length n is equivalent to a quasi-cyclic code.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.6 pp.1863-1865
- Publication Date
- 2006/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e89-a.6.1863
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Keyword
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Jian-Fa QIAN, Li-Na ZHANG, Shi-Xin ZHU, "Constacyclic and Cyclic Codes over F2+uF2+u2F2" in IEICE TRANSACTIONS on Fundamentals,
vol. E89-A, no. 6, pp. 1863-1865, June 2006, doi: 10.1093/ietfec/e89-a.6.1863.
Abstract: A new Gray map between codes over F2+uF2+u2F2 and codes over F2 is defined. We prove that the Gray image of a linear (1-u2)-cyclic code over F2+uF2+u2F2 of length n is a binary distance invariant linear quasi-cyclic code. We also prove that, if n is odd, then every binary code which is the Gray image of a linear cyclic code over F2+uF2+u2F2 of length n is equivalent to a quasi-cyclic code.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.6.1863/_p
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@ARTICLE{e89-a_6_1863,
author={Jian-Fa QIAN, Li-Na ZHANG, Shi-Xin ZHU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Constacyclic and Cyclic Codes over F2+uF2+u2F2},
year={2006},
volume={E89-A},
number={6},
pages={1863-1865},
abstract={A new Gray map between codes over F2+uF2+u2F2 and codes over F2 is defined. We prove that the Gray image of a linear (1-u2)-cyclic code over F2+uF2+u2F2 of length n is a binary distance invariant linear quasi-cyclic code. We also prove that, if n is odd, then every binary code which is the Gray image of a linear cyclic code over F2+uF2+u2F2 of length n is equivalent to a quasi-cyclic code.},
keywords={},
doi={10.1093/ietfec/e89-a.6.1863},
ISSN={1745-1337},
month={June},}
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TY - JOUR
TI - Constacyclic and Cyclic Codes over F2+uF2+u2F2
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1863
EP - 1865
AU - Jian-Fa QIAN
AU - Li-Na ZHANG
AU - Shi-Xin ZHU
PY - 2006
DO - 10.1093/ietfec/e89-a.6.1863
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2006
AB - A new Gray map between codes over F2+uF2+u2F2 and codes over F2 is defined. We prove that the Gray image of a linear (1-u2)-cyclic code over F2+uF2+u2F2 of length n is a binary distance invariant linear quasi-cyclic code. We also prove that, if n is odd, then every binary code which is the Gray image of a linear cyclic code over F2+uF2+u2F2 of length n is equivalent to a quasi-cyclic code.
ER -
English
