Weight hierarchies of three-weight p-ary linear codes from inhomogeneous quadratic forms

05/03/2023

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by   Shupeng Hu, et al.

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The weight distribution and weight hierarchy of a linear code are two important research topics in coding theory. In this paper, choosing D={(x,y)∈(_p^s_1×_p^s_2)\{(0,0)}: f(x)+_1^s_2(α y)=0} as a defining set , where α∈𝔽_p^s_2^* and f(x) is a quadratic form over 𝔽_p^s_1 with values in _p, whether f(x) is non-degenerate or not, we construct a family of three-weight p-ary linear codes and determine their weight distributions and weight hierarchies. Most of the codes can be used in secret sharing schemes.