Signed difference sets have interesting applications in communications and coding theory. A \((v,k,\lambda )\)-difference set in a finite group G of order v is a subset D of G with k distinct elements such that the expressions \(xy^{-1}\) for all distinct two elements \(x,y\in D\), represent each non-identity element in G exactly \(\lambda \) times. A \((v,k,\lambda )\)-signed difference set is a generalization of a \((v,k,\lambda )\)-difference set D, which satisfies all properties of D, but has a sign for each element in D. We will show some new existence results for signed difference sets by using partial difference sets, product methods, and cyclotomic classes.

有符号差集在通信和编码理论中有有趣的应用。v阶有限群G中的\((v,k,\lambda )\)差分集是G的子集D，具有k 个不同元素，使得所有的表达式\(xy^{-1}\) D 中不同的两个元素\(x,y\)恰好代表G中每个非同一元素的\(\lambda \)次。一个\((v,k,\lambda )\)有符号差分集是一个\((v,k,\lambda )\)差分集D的泛化，它满足D的所有属性，但有一个符号对于D中的每个元素。我们将通过使用偏差集、乘积方法和分圆类来展示有符号差集的一些新的存在性结果。