基于二次乘法特征的射影线性码

Two families of linear codes are constructed based on the quadratic multiplicative characters of finite fields. The parameters and weight distributions of the codes are explicitly determined. It turns out that the first family of linear codes are projective three-weight ones whose duals are almost optimal according to the sphere-packing bound. The second family of linear codes are projective two-weight ones whose duals are also almost optimal according to the sphere-packing bound. Besides, some self-orthogonal codes and minimal codes are obtained. The self-orthogonal codes can be used to construct quantum codes and minimal codes can be used to construct secret sharing schemes with safe and sufficient access structures.