Z_(2~a)+uZ_(2~a)上线性码的MacWilliams恒等式及自对偶码
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摘要
考虑环R=Z2a+uZ2a上的线性码,其中u2=u。研究了环R上线性码的完全Gray权估计的M ac Williams恒等式。给出了环R上的自对偶码的生成矩阵及环Z23+u Z23上长为偶数n的自对偶码的数量公式。讨论了环R上的挠码,得到挠码的生成矩阵及挠码与剩余码的关系。
The linear codes over R = Z2 a+ u Z2 awith u2= u are discussed. Mac Williams identity for the complete Gray weight enumerator is investigated firstly. Then,the generator matrices of self-dual codes over R and the number of distinct self-dual codes of even length n over Z23+ u Z23 are given. The torsion codes over R are discussed and the generator matrices of torsion codes and the relationship between the torsion codes and the residue codes are also obtained.
The linear codes over R = Z2 a+ u Z2 awith u2= u are discussed. Mac Williams identity for the complete Gray weight enumerator is investigated firstly. Then,the generator matrices of self-dual codes over R and the number of distinct self-dual codes of even length n over Z23+ u Z23 are given. The torsion codes over R are discussed and the generator matrices of torsion codes and the relationship between the torsion codes and the residue codes are also obtained.
引文
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[7]张莉娜,殷志祥.Zpm环上的自对偶码与么模格的构造[J].通信技术,2009,42(2):42-43.ZHANG Lina,YIN zhixiang.Self-dual codes over Zpm and construction of unimodular lattices[J].Communications Technology,2009,42(2):42-43.
[8]NAGATA Kiyoshi,NEMENZO Fidel,WADA Hideo.The number of self-dual codes over Zp3[J].Designs Codes and Cryptography,2009,50(3):291-303.
[2]WAN Zhexian.Quaternary codes[M].Singapore:World Scientific Publishing Co Pte Ltd,1997:25-68.
[3]RAINS Eric.Bound for self dual codes over Z4[J].Finite Fields and Their Applications,2000,6(2):146-163.
[4]朱士信.Zk线性码的对称形式的Mac Williams恒等式[J].电子与信息学报,2003,25(7):901-906.ZHU Shixin.A symmetrized M ac Williams identity of Zk-linear code[J].Journal of Electronics and Information Technology,2003,25(7):901-906.
[5]YILDIZ B,Karadeniz S.Linear codes over Z4+u Z4:Mac Williams identities,projections,and formally self-dual codes[J].Finite Fields Appl,2014,27:24-40.
[6]GAO Jian,WANG Xianfang,FU Fangwei.Self-dual codes and quadratic residue codes over Z9+u Z9[J/OL].[2014-12-10].http://arxiv.org/pdf/1405.3347v2.pdf.
[7]张莉娜,殷志祥.Zpm环上的自对偶码与么模格的构造[J].通信技术,2009,42(2):42-43.ZHANG Lina,YIN zhixiang.Self-dual codes over Zpm and construction of unimodular lattices[J].Communications Technology,2009,42(2):42-43.
[8]NAGATA Kiyoshi,NEMENZO Fidel,WADA Hideo.The number of self-dual codes over Zp3[J].Designs Codes and Cryptography,2009,50(3):291-303.