环F_(p^k)+uF_(p^k)+u^2F_(p^k)上的常循环码和循环码

Constacyclic and Cyclic Codes over F_(p^k) + uF_(p~κ)+u^2F_(p^k)

记环R=F_(p^k)+uF_(p^k)+u^2F_(p^k),定义了一个从R^n到F_(p^k)^(2np^k)的Gray映射.利用Gray映射的性质,研究了环R上(1-u^2)-循环码和循环码.证明了环R上码是(1-u^2)-循环码当且仅当它的Gray象是F_(p^k)上的准循环码.当(n,p)=1时,证明了环R上的长为n的线性循环码的Gray象置换等价于域F_(p^k)上的线性准循环码.

F2npk Let R = Fpk ＋ uFpk ＋ u2Fpk, a Gray map from Rn to Fpk^2npk is defined. Base on the property of Gray map, （1 - u2）-cyclic and cyclic codes over R are studied. It is proved that a code over R is a （1 - u2）-cyclic code if and only if its Gray image is a quasi-cyclic code over Fpk. It is also proved that if （n,p） = 1, the Gray image of a linear cyclic code of length n over R is equivalent to a linear quasi-cyclic code over Fpk.