Cyclic codes and self-dual codes over F2+uF2+u2F2+u3F2

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (11): 26-29.

• 研究、探讨 • Previous Articles Next Articles

Cyclic codes and self-dual codes over F₂+uF₂+u²F₂+u³F₂

YAN Guoqi，XIN Xiaolong

Department of Mathematics，Northwest University，Xi’an 710127，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-04-11 Published:2011-04-11

F₂+uF₂+u²F₂+u³F₂上的循环码和自对偶码

闫国旗，辛小龙

西北大学数学系，西安 710127

Abstract

Abstract: A finite ring with 16 elements is constructed and a necessary condition for a finite ring code with odd length becoming cyclic code is given.Furthermore，a generator polynomial of the finite ring code with odd length is obtained，and finally a necessary and sufficient condition for the existence of the self-dual codes of the finite ring is eventually proved.

Key words: finite ring, ideal, cyclic code, self-dual code

摘要： 构造了一个含有16个元素的有限环，给出了这个有限环上码长为奇数的循环码的必要条件。然后给出了这个有限环上码长为奇数的循环码的一个生成多项式，得到了在这个环上的自对偶码存在的一个充分必要条件。

关键词: 有限环, 理想, 循环码, 自对偶码

YAN Guoqi，XIN Xiaolong. Cyclic codes and self-dual codes over F₂+uF₂+u²F₂+u³F₂[J]. Computer Engineering and Applications, 2011, 47(11): 26-29.

闫国旗，辛小龙. F₂+uF₂+u²F₂+u³F₂上的循环码和自对偶码[J]. 计算机工程与应用, 2011, 47(11): 26-29.

[1]	WANG Fengxiao. Interval-value fuzzy ideals of incline algebras [J]. Computer Engineering and Applications, 2018, 54(9): 54-56.
[2]	HUANG Yu1, LIAO Zuhua2, LI Lun3. New type of soft positive implicative ideals of weak-BCI-algebras [J]. Computer Engineering and Applications, 2018, 54(21): 31-36.
[3]	LIU Chunhui. IV-fuzzy ideals in negative non-involutive residuated lattices [J]. Computer Engineering and Applications, 2018, 54(18): 40-44.
[4]	MENG Biaolong, FU Qiaofeng, LIANG Shaohui. Minimal prime ideals and [α]-ideals in lattice implication algebras [J]. Computer Engineering and Applications, 2018, 54(16): 44-48.
[5]	PENG Jiayin. Hesitant fuzzy filters and hesitant fuzzy ideals of BR0 algebras [J]. Computer Engineering and Applications, 2018, 54(11): 62-66.
[6]	WANG Lunlei, WU Hongbo. Annihilator operators and[⊕]ideals of IMTL-algebra with their relationships [J]. Computer Engineering and Applications, 2017, 53(9): 57-62.
[7]	HAN Jiao1, QU Yunyun2, BAO Xiaomin1. Gray codes based weight distribution generating algorithm [J]. Computer Engineering and Applications, 2017, 53(23): 51-53.
[8]	FU Xiaobo. Ω-Fuzzy LI-ideals in lattice implication algebras [J]. Computer Engineering and Applications, 2017, 53(22): 50-54.
[9]	SHANG Yufang, LIANG Xiangqian, SUN Yiru. Identity-based proxy re-signature over ideal lattice [J]. Computer Engineering and Applications, 2017, 53(21): 110-114.
[10]	PENG Xindong, YANG Yong. Multiple attribute group decision making methods based on Pythagorean fuzzy linguistic set [J]. Computer Engineering and Applications, 2016, 52(23): 50-54.
[11]	WANG Caifen, DENG Yunxia, Niu Shufen. New attribute-based encryption on ideal lattices [J]. Computer Engineering and Applications, 2016, 52(17): 123-127.
[12]	YU Haifeng, ZHANG Xia. (1+u+v)-cyclic codes over Fp+uFp+vFp [J]. Computer Engineering and Applications, 2016, 52(1): 110-112.
[13]	LIAO Zuhua1，3，4, WANG Nini2，3，4, ZHENG Gaoping1，3，4, ZHANG Licheng1，3，4. Soft filters of lattice implication algebra [J]. Computer Engineering and Applications, 2015, 51(9): 72-76.
[14]	ZHENG Gaoping1，3，4, LIAO Zuhua1，3，4, WANG Nini2，3，4, ZHANG Licheng1，4. Soft LI-ideals of lattice implication algebra [J]. Computer Engineering and Applications, 2015, 51(8): 42-46.
[15]	LIU Chunhui1，2. Idealistic soft BCK-algebras based on interval valued fuzzy sets [J]. Computer Engineering and Applications, 2015, 51(22): 66-69.

Cyclic codes and self-dual codes over F₂+uF₂+u²F₂+u³F₂

F₂+uF₂+u²F₂+u³F₂上的循环码和自对偶码

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics