Weight hierarchies of a class of three-weight $p$-ary linear codes from inhomogeneous quadratic functions
Weight hierarchies of a class of three-weight $p$-ary linear codes from inhomogeneous quadratic functions
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DOI：
10.1007/s00200-024-00645-7
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发表时间：
2024
期刊：
影响因子：
--
通讯作者：
李修美
中科院分区：
文献类型：
--
作者：
胡舒鹏;李斐;李修美
The weight hierarchy of a linear code have been an important research topic in coding theory since Wei's original work in 1991..In this paper, choosing $ D=\Big\{(x,y)\in \Big(\F_{p^{s_1}}\times\F_{p^{s_2}}\Big)\Big\backslash\{(0,0)\}: f(x)+\Tr_1^{s_2}(\alpha y)=0\Big\}$ as a defining set ,.where $\alpha\in\mathbb{F}_{p^{s_2}}^*$, $f(x)$ is a quadratic form over $\mathbb{F}_{p^{s_1}}$ with values in $\F_p$ and $f(x)$ can be non-degenerate or not,.we construct a family of three-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.
