环F_(p^m)+uF_(p^m)上长为p^k的循环码计数

Mass Formulas for Cyclic Codes of Length p^k over the Ring F_(p^m)+uF_(p^m)

环R=Fpm+uFpm上长为pk的循环码可看作R[x]/<xpk-1>上的理想。该文通过对R[x]/<xpk-1>上理想的研究,得到了环Fpm+uFpm上长为pk的循环码的唯一表示方法和计数,并给出了该环上长为pk的循环自对偶码的结构和计数。

Cyclic codes over the ringR = Fp m ＋ uFpm can be seen as the ideals of R[x]/xpk-1. Based on the studing of ideals of R[x]/ xpk-1 ,a unique method of representing cyclic codes of length pk and their mass formulas over the ring Fpm ＋ uFpm are provided. For the cyclic self-dual codes of length pk over the ring Fpm ＋ uFpm,their structures and mass formulas are given.