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arXiv · 2003.03048

Weight hierarchies and weight distributions of a familiy of $p$-ary linear codes

Fei Li·Xiumei Li
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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.

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Fei Li, Xiumei Li. 2020-03-06. Weight hierarchies and weight distributions of a familiy of $p$-ary linear codes. https://doi.org/10.1007/s10623-021-00962-9

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