环F_p+uF_p+vF_p+uvF_p上线性码的Gray像

The Gray Images of the Linear Codes Over the Ring F_p+uF_p+vF_p+uvF_p

定义了有限非链环R=F_p+uF_p+vF_p+uvF_p到F_p^4的一个Gray映射.在证明了该映射是R^n到F_p^(4n)的等重等距映射的基础上进一步证明了环R上的线性码C的Gray像是距离不变码.特别地如果C是环F_2+uF_2+vF_2+uvF_2上的Lee恒距线性码,则Φ(C)为F_2上的Hamming恒距线性码.最后通过映射Ψ把F_p+uF_p上的线性码和R上的一类线性码对应起来.

In this paper, the Gray map Ф form R -- Fp＋uFp＋vFp＋uvFp to Fp4 is given, where the ring R is not a finite chain ring. Then, the Gray map Ф is proved to be weight-preserving and distance-preserving. The Gray image of a linear code C over ring F2 ＋ uF2 ＋vF2 ＋ uvF2, called Ф（C） is Hamming distance invariant, if C is Lee distance invariant. Finally, by the map ψ, linear codes over Fp ＋ uFp are correspond to a class of linear codes over R.