摘要
本文定义了环F2+uF2+vF2到域F2的广义Gray映射φ像,研究了环F2+uF2+vF2上线性码的广义Gray像.利用广义Gray映射φ的线性性,证明了环F2+uF2+vF2上线性码C的广义Gray像φ(C)满足dH(C)=dH(φ(C))且φ(C⊥)φ(C)⊥.同时,给出了F2+uF2+vF2上循环码C的广义Gray像φ(C)为F2上的4-拟循环码.
The generalized Grayφis defined from F2＋uF2＋vF2 to F4 n 2.The generalized Gray images of linear codes over F2＋uF2＋vF2 are studied.By using the linearlity of the generality Grayφ,it is proved that the generalized Gray imagesφ（C）of linear codes C over F2＋uF2＋vF2 are linear codes over F2 and dH（C）=dH（φ（C））.Furthermore,we obtain that φ（C⊥）φ（C）⊥and the generalized Gray imagesφ（C）of cyclic codes C over F2＋uF2＋vF2 are the 4-quasi-cyclic codes over F2.
出处
《数学杂志》
CSCD
北大核心
2012年第3期567-570,共4页
Journal of Mathematics
