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

06/13/2023

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by   Xiumei Li, et al.

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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)∈(_p^s_1×_p^s_2)\{(0,0)}: f(x)+g(y)=0} as a defining set , where f(x),g(y) are quadratic forms over 𝔽_p^s_i,i=1,2, respectively, with values in _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.