中文摘要：

设R=F_p＋uF_p＋vF_p＋uvF_p＋v~2F_p＋uv~2F_p,其中u~2=1,v~3=v,p是一个奇素数.研究了环R上素长度n=q的二次剩余码,其中q（q≠p）是一个奇素数且p是模q的二次剩余.首先研究了环R上长度为n的循环码,根据其幂等生成元定义了环R上的二次剩余码,进一步讨论了该环上二次剩余码与其扩展码的关系.最后,为了验证结果的正确性,给出了F_p＋uF_p＋vF_p＋uvF_p＋v~2F_p＋uv~2F_p上二次剩余码的幂等生成元的两种具体形式.

英文摘要：

Let R=F_p＋uF_p＋vF_p＋uvF_p＋v~2F_p＋uv~2F_p,where u~2=1,v~3=v,and pis an odd prime.Quadratic residue codes of prime length n=q over the ring R was investigated,where q（q≠p）is an odd prime such that pis aquadratic residue modulo q.The cyclic codes of length n over R were studied,and then the quadratic residue codes over R in terms of idempotent generators were difined.Moreover,the relation between these codes and their extended codes are discussed.Finally,two specific forms of idempotent generators of quadratic residue codes over F_p＋uF_p＋vF_p＋uvF_p＋v~2F_p＋uv~2F_p were given to illustrate some results.