Research on combinatorics over Galois rings

构造了特征为2的偶次幂的伽罗瓦环上的差集无限族。特征为2^n的伽罗瓦环上的差集嵌入特征为2^n+2的伽罗瓦环上的差集的理想部分。在Galois环中引入了一种新的运算，在这种新的运算下特征标的高斯和在证明中起着重要的作用。进一步证明了具有嵌入系的Reed-Muller码的存在性，并给出了这类码的一些性质。

We constructed infinite families of difference sets over Galois rings of characteristic an even power of 2. The difference set over a Galois ring of characteristic 2^n is embedded in the ideal part of the difference set over a Galois ring of characteristic 2^n+2 . We introduced a new operation in a Galois ring and the Gauss sums associated with the character under this new operation play an important role of the proof. Furthermore, we proved there exist Reed-Muller codes with embedding system and showed several properties of them.