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环${Z}_{ 4}+{u}{Z}_{ 4}$上一类重根常循环码

李兰强,刘丽   

  1. 合肥工业大学,合肥  230009
  • 出版日期:2017-03-25 发布日期:2017-04-28

李兰强,刘丽. 环${Z}_{ 4}+{u}{Z}_{ 4}$上一类重根常循环码[J]. 系统科学与数学, 2017, 37(3): 870-881.

LI Lanqiang,LIU Li. A Family of Repeated-Root Constacyclic Codes over ${\bm Z}_{\bf 4}+{\bm u{\bm Z}}_{\bf 4}[J]. Journal of Systems Science and Mathematical Sciences, 2017, 37(3): 870-881.

A Family of Repeated-Root Constacyclic Codes over ${\bm Z}_{\bf 4}+{\bm u{\bm Z}}_{\bf 4}

LI Lanqiang ,LIU Li   

  1. School of Mathematics, Hefei University of Technology, Hefei 230009
  • Online:2017-03-25 Published:2017-04-28

设$R=Z_4+uZ_4$, $R_n={R[x]}/{(x^n-(2u-1))}$, 其中$u^2=0$, $n=2^e$. 通过对环$R$上码长为$n$的$(2u-1)$-常循环码结构的研究, 得到这些码的生成元, 并对环$R$上码长为$n$的所有$(2u-1)$-常循环码进行分类, 而且研究了该环上$(2u-1)$-常循环码的Hamming距离分布. 最后给出环$R$上码长为$n$的$(2u-1)$-常循环码的对偶码的结构以及环$R$上码长为$n$的自正交与自对偶的$(2u-1)$-常循环码.

Let $R=Z_4+uZ_4$, $R_n={R[x]}/{(x^n-(2u-1))}$, where $u^2=0$, $n=2^e$. By studying the structures of $(2u-1)$-constacyclic codes over $R$ of length $n$, we obtain the generators for these codes and classify all $(2u-1)$-constacyclic codes of length $n$ over $R$. Further, we study the Hamming distance distributions of $(2u-1)$-constacyclic codes of length $n$ over $R$. Finally, we give the structures of the duals of $(2u-1)$-constacyclic codes over $R$ of length $n$ and self-orthogonal and self-dual $(2u-1)$-constacyclic codes of length $n$ over $R$.

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