中文摘要：

该文利用有限环Fq＋uFq 上循环自正交码，给出了一种构造有限域Fq上自正交码的方法。引入了Fq＋uFq到Fqp的等距Gray映射，给出了Fq＋uFq上循环自正交码存在的充分必要条件，证明了Fq＋uFq 上长为n的循环自正交码的Gray象是Fq上长为pn的自正交码，由此构造了Fq上一些参数较好的自正交码。

英文摘要：

A method is proposed to construct self-orthogonal codes over the finite field Fq by using cyclic self-orthogonal codes over the finite ring q qF ？uF . A Gray map from q qF ？uF to pqF is introduced, and a sufficient and necessary condition for the existence of cyclic self-orthogonal codes over q qF ？uF is given. It is proved that the Gray image of a cyclic self-orthogonal code with length n over q qF ？uF is a self-orthogonal code with length pn over Fq . Further, some self-orthogonal codes over Fq with good parameters are constructed.