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<p>We give upper bounds on the covering radius of special low rate codes (repetition, Simplex, and MacDonald) over <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2574_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{Z}_q\)</EquationSource> </InlineEquation>, with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2574_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(q\)</EquationSource> </InlineEquation> a prime power, for the Lee, euclidean and homogeneous distance and compare them to the relevant sphere covering bounds in modest lengths.</p>

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The covering radius for the Lee, euclidean and homogeneous distance of the Simplex codes and related codes

  • 期刊论文

  • 发表日期：

    2025年7月21日

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  • Minjia Shi,
  • Xingxing Xu,
  • Patrick Solé

摘要

We give upper bounds on the covering radius of special low rate codes (repetition, Simplex, and MacDonald) over \(\mathbb{Z}_q\) , with \(q\) a prime power, for the Lee, euclidean and homogeneous distance and compare them to the relevant sphere covering bounds in modest lengths.