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中文摘要：
研究了环R=Fl＋vFl（其中v2=v,且l是奇素数）上的二次剩余码.首先研究了环R上长为n的循环码,然后用生成幂等元的形式定义了环R上二次剩余码,并讨论了它们与其扩展码之间的关系和对偶等性质.进一步,定义并研究了环R上二次剩余码的极小Lee距离,结果表明环R上二次剩余码具有良好的参数.特别地,确定了F3＋vF3上码长为11的二次剩余码的幂等生成元的具体形式和它们的极小Lee距离.
英文摘要：
Quadratic residue codes over the ring R=Fl＋vFl was investigated,where v2=v and l is an odd prime.Cyclic codes of length n over R was studied first.Then,quadratic residue codes over R was defined by their generating idempotents,and the relations between these codes and their extended codes were discussed.Their properties,including their duality were also studied.Further,their minimum Lee distance was defined and investigated,and good parameters were shown.In particular,the specific forms of generating idempotents of quadratic residue codes of length 11 over F3＋vF3 were determined,and its minimum Lee distance was considered.
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