Weight hierarchies of 3-weight linear codes from two $p$-ary quadratic functions

The weight hierarchy of a linear code has been an important research topic in coding theory since Wei’s original work in 1991. Choosing $D=\{(x,y)\in ({\text{F}}_{p^{s_1}}\times {\text{F}}_{p^{s_2}})\backslash \{(0,0)\}:f(x)+g(y)=0\}$ as a defining set , where $f(x),g(y)$ are quadratic forms over ${\mathbb{F}}_{p^{s_i}},i=1,2$, respectively, with values in ${\text{F}}_p$, we construct a family of 3-weight $p$-ary linear codes and determine their weight distributions and weight hierarchies completely. Most of the codes can be used in secret sharing schemes.