Abstract: It is given that an another proof for the classical affine relative difference set by using Gauss sums, and we construct a new family of divisible difference sets with parameters ((qⁿ-1)/(q-1), q-1, q^(n-1)-1, q^(n-1)-1, q^(n-2)-1), where n≥2, q is a power of a prime.

Key words: relative difference sets, divisible difference sets, character, Gauss sums, inversion formula

摘要： 给出了经典的仿射相对差集的一个特征标方法的证明。构造了一族新的可分差集，具有参数 ((qⁿ-1)/(q-1), q-1, q^(n-1)-1, q^(n-1)-1, q^(n-2)-1), 其中n≥2, q为素数幂。

关键词: 相对差集, 可分差集, 特征标, Gauss和, 反演公式