环F2+uF2+…+uk-1F2上常循环自对偶码

doi:10.3969/j.issn.0372-2112.2013.06.008

电子学报 ›› 2013, Vol. 41 ›› Issue (6): 1088-1092.DOI: 10.3969/j.issn.0372-2112.2013.06.008

环F₂+uF₂+…+u^k-1F₂上常循环自对偶码

施敏加

安徽大学数学科学学院, 安徽合肥 230601

收稿日期:2011-08-15 修回日期:2012-12-28 出版日期:2013-06-25
- 作者简介:
- 施敏加男,1980年生于安徽枞阳,博士,安徽大学数学科学学院副教授,硕士生导师,主要研究方向为代数编码与密码. E-mail:mjshi@ahu.edu.cn
- 基金资助:
- 国家自然科学基金 (No.61202068,No.11126174); 安徽省高校优秀青年人才基金重点项目 (No.2012SQRL0202D)

Constacyclic Self-Dual Codes over Ring F₂+uF₂+…+u^k-1F₂

SHI Min-jia

School of Mathematics Sciences of Anhui University, Hefei, Anhui 230601, China

Received:2011-08-15 Revised:2012-12-28 Online:2013-06-25 Published:2013-06-25
- Supported by:
- National Natural Science Foundation of China (No.61202068, No.11126174); Key Program of Outstanding Young Talents Fund in Colleges and Universities of Anhui Province (No.2012SQRL0202D)

摘要/Abstract

摘要： 最近,剩余类环上的常循环码及常循环自对偶码引起了编码学者的极大关注.本文首先利用一些相关的线性码,建立了一类特殊有限链环上长为N的常循环自对偶码的一般理论,利用其结果给出了该环上长为N的(1+uλ)-常循环自对偶码存在的充分条件,得到了该环上长为N的一些常循环自对偶码,并给出了其生成多项式.

关键词: 常循环码, 对偶码, 自正交码, 分圆陪集

Abstract: Recently,a lot of coding scholars show a great interest in the study of constacyclic codes and constacyclic self-dual codes over the residue rings.In this paper,by utilizing some related linear codes,we first give the general theory of constacyclic self-dual codes of length N over a class of special finite chain rings.Using the obtained results,we give the sufficient conditions of the existence of constacyclic self-dual codes of length N over the ring.Finally,we determine the structures of some constacyclic self-dual codes of length N over the ring and give their generator polynomials.

Key words: constacyclic codes, dual codes, self-orthogonal codes, cyclotomic cosets

中图分类号:

TN911.22

施敏加. 环F₂+uF₂+…+u^k-1F₂上常循环自对偶码[J]. 电子学报, 2013, 41(6): 1088-1092.

SHI Min-jia . Constacyclic Self-Dual Codes over Ring F₂+uF₂+…+u^k-1F₂[J]. Acta Electronica Sinica, 2013, 41(6): 1088-1092.

参考文献

[1] S X Zhu,X S Kai.A class of constacyclic codes over Z_p^m[J].Finite Fields and Their Application,2010,16(4):243-254.

[2] J F Qian,L N zhang,S X Zhu.(1+u)-constacyclic and cyclic codes over F₂+uF₂[J].Applied Mathematics Letter,2006,19(8):820-823.

[3] M C V Amarra,F R Nemenzo.On (1-u)-cyclic codes over F_p^k+uF_p^k[J].Applied Mathematics Letter,2008,21(11):1129-1133.

[4] T abualrub,I Siap.Constacyclic codes over F₂+uF₂[J].Journal of the Franklin Institute,2009,346(5):520-529.

[5] Shi Minjia,Zhu Shixin.Constacyclic codes over ring F_q+uF_q+…+u^s-1F_q[J].中国科学技术大学学报,2009,39(6):583-587.

[6] 朱士信,李平,吴波.环F_q+uF_q+…+u^k-1F_q上一类重根常循环码[J].电子与信息学报,2008,30(6) :1394-1396.

[7] X S Kai,S X Zhu,Ping Li.(1+λu)-Constacyclic codes over F_p/< u^k >[J].Journal of the Franklin Institute,2010,347(5):751-762.

[8] H Q Dinh.Constacyclic codes of length 2^s over Galois extension rings F₂+uF₂[J].IEEE Trans Inform Theory,2009,55(4):1730-1740.

[9] H Q Dinh.Constacyclic codes of length p^s over Galois extension rings of F_p^m+uF_p^m[J].Journal of Algebra,2010,324(5):940-950.

[10] X S Kai,S X Zhu.On cyclic self-dual codes[J].Applicable Algebra in Engineering,Communication and Computing,2008,19(6):509-525.

[11] B Heijne,J Top.On the minimal distance of binary self-dual cyclic codes[J].IEEE Trans Inform Theory,2009,55(11):4860-4863.

[12] Yan jia,San Ling,Chaoping Xing.On self-dual cyclic codes over finite fields[J].IEEE Trans Inform Theory,2011,57(4):2243-2251.

[13] P Kanwar,S R López-permauth.Cyclic codes over the integers modulo p^m[J].Finite Fields and Their Application,1997,3(4):334-352.

[14] V S Pless,P Solé,Z Qian.Cyclic self-dual Z₄-codes[J].Finite Fields and Their Application,1997,3(1):48-69.

[15] X S Kai,S X Zhu.Negacyclic self-dual codes over finite chain rings[J].Designs,Codes and Cryptography,2012,62(2):161-174.

[16] 施敏加,杨善林,朱士信.F₂+uF₂上长为2^e的循环码的距离[J].电子学报,2011,39(1):29-34. Shi Min-jia,Yang Shan-lin,Zhu Shi-xin.On minimum distances of cyclic codes of length 2^e over F₂ +u F₂[J].Acta Electronica Sinica,2011,39(1):29-34.(in Chinese)

[17] 施敏加,杨善林,朱士信.环F₂+uF₂+…+u^k-1F₂上长为2^s的(1+u)-常循环码的距离分布[J].电子与信息学报,2010,32(1):112-116.

[18] G H Norton,A S?l?gean.On the structure of linear and cyclic codes over a finite chain ring[J].Applicable Algebra in Engineering,Communication and Computing,2000,10(6):489-506.

[19] G H Norton,A S?l?gean.On the Hamming distance of linear codes over finite chain rings[J].IEEE Trans Inform Theory,2000,46(3):1060-1067.

环F₂+uF₂+…+u^k-1F₂上常循环自对偶码

Constacyclic Self-Dual Codes over Ring F₂+uF₂+…+u^k-1F₂

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