环Fq+uFq+vFq上的斜循环码和LCD码
SKEW CYCLIC AND LCD CODES OVER Fq+uFq+vFq

本文研究了环R=Fq+uFq+vFq（u2=u，v2=v，uv=vu=0）上的斜循环码和LCD码，其中q为素数幂.利用线性码与其对偶码在环R上的分解，得到了环R上斜循环码及其对偶码的生成多项式.最后，讨论了环R与有限域Fq上LCD码的关系，通过环R到域Fq3的Gray映射，得到了环R上LCD码的Gray像是Fq上的LCD码.
In this paper, we investigate skew cyclic and LCD codes over the ring R=Fq+uFq+vFq(u2=u,v2=v,uv=vu=0), where q is a prime power. Using some decompositions of linear codes and their duals over ring R, we obtain the generator polynomials of skew cyclic and their dual codes over R. Finally, we address the relationship of LCD codes between R and Fq. By means of the Gray map from R to Fq3, we obtain that Gray images of LCD codes over R are LCD codes over Fq