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Weight hierarchies and weight distributions of a familiy of $p$-ary linear codes (2003.03048v2)
Published 6 Mar 2020 in cs.IT, math.IT, and math.NT
Abstract: The weight distribution and weight hierarchy of linear codes are two important research topics in coding theory. In this paper, by choosing proper defining sets from inhomogeneous quadratic functions over $\mathbb{F}_{q}{2},$ we construct a family of $3$-weight $p$-ary linear codes and determine their weight distributions and weight hierarchies. Most of the codes can be used in secret sharing schemes.