摘要
在环F2+uF2上定义了一个新变换τ(a)=(eiπu)a,其中,i2=-1,a∈F2+uF2.研究了环F2+uF2上线性码的Lee完全Rosenbloom-Tsfasman(RT)重量计数器,给出了环F2+uF2上线性码关于这种重量计数器的MacWilliams恒等式.利用该恒等式不必求出环F2+uF2上线性码C的对偶码C⊥,即可得到对偶码C⊥的Lee完全RT重量计数器.
A new transform r（a）- （eiu^ ）a （where ix =- 1, a ∈ F2 ＋uF2） and the definition of the Lee complete ρ weight enumerator were given. Furthermore, the MacWilliams identity with respect to this Rosenbloom-Tsfasman metric for the Lee complete ρ weight enumerator was proven. It is not necessary, according to the identity, to obtain the dual code C⊥ of the liner code C over the ring F2 ＋uF2, thus the Lee complete ρ weight enumerator of the dual code C⊥ can be directly obtained.
基金
浙江省教育厅基金(Y201326745)
国家社会科学基金(12BTJ005)资助
