Some three-weight linear codes and their complete weight enumerators and weight hierarchies

Xiumei Li; Zongxi Chen; Fei Li

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arXiv · 2410.02209

Some three-weight linear codes and their complete weight enumerators and weight hierarchies

Xiumei Li·Zongxi Chen·Fei Li

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Abstract

Linear codes with a few weights can be applied to secrete sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power $q$, we construct a class of three-weight $\F_q$-linear codes from quadratic functions via a bivariate construction and then determine the complete weight enumerators and weight hierarchies of these linear codes completely. This paper generalizes some results in Li et al. (2022) and Hu et al. (2024).

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Xiumei Li, Zongxi Chen, Fei Li. 2024-10-03. Some three-weight linear codes and their complete weight enumerators and weight hierarchies. https://arxiv.org/abs/2410.02209

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