环F_2+uF_2+u^2F_2上的常循环码和循环码的Gray象

The Gray Images of Constacyclic and Cyclic Codes over F_2+uF_2+u^2F_2

通过构造Gray映射Φ,研究了环R=F2+uF2+u2F2上的常循环码和循环码.给出了环R上码是常循环码的一个充分必要条件,证明了环R上长为n的码C是循环码当且仅当Φ(C)是域F2上指标为4长为4n的准循环码.特别的,环R上长为n的线性循环码的Gray像是F2上指标为4长为4n的线性准循环码.

By constructing the Gray map Φ,constacyclic and cyclic codes over the ring R=F2＋uF2＋u2F2 are studied.A necessary and sufficient condition for a code to be constacyclic over R is given.It is proved that a code C of length n over R is a cyclic code if and only if Φ（C） is a quasi-cyclic code over F2 of index 4 and length 4n. In particular,the Gray image of a linear cyclic code of length n over R is a linear quasi-cyclic code of index 4 and length 4n over F2.