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<p>Linear codes with a few weights can be applied to secret sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power <i>q</i>, we construct a class of three-weight <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {F}_q\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation>-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) [<CitationRef CitationID="CR30">30</CitationRef>] and Hu et al. (2024) [<CitationRef CitationID="CR20">20</CitationRef>].</p>

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

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Xiumei Li,
  • Zongxi Chen,
  • Fei Li

摘要

Linear codes with a few weights can be applied to secret sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power q, we construct a class of three-weight \(\mathbb {F}_q\) 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) [30] and Hu et al. (2024) [20].