<p>This article investigates the application of a Gray map and Gray images in the context of linear codes over <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3082_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathfrak {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">R</mi> </math></EquationSource> </InlineEquation>. It explores the properties and utility of linear codes within this framework, including their role in constructing LCD codes. Furthermore, the article examines the implementation of multi-secret sharing schemes using LCD codes over <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3082_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathfrak {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">R</mi> </math></EquationSource> </InlineEquation>. It also provides a comprehensive analysis and assessment of the security features of these codes, offering insights into their strength and robustness.</p>

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Application of multi-secret sharing schemes using LCD codes over \(\mathfrak {R}=\mathcal {R}\left[ w\right] \)

  • Karima Chatouh,
  • Dejia Mokhtari,
  • Kenza Guenda

摘要

This article investigates the application of a Gray map and Gray images in the context of linear codes over \(\mathfrak {R}\) R . It explores the properties and utility of linear codes within this framework, including their role in constructing LCD codes. Furthermore, the article examines the implementation of multi-secret sharing schemes using LCD codes over \(\mathfrak {R}\) R . It also provides a comprehensive analysis and assessment of the security features of these codes, offering insights into their strength and robustness.