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<p>In this paper, we investigate negacyclic dually-BCH codes over <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_785_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textbf{GF}\varvec{(q)}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">GF</mi> <mrow> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">q</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of length <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_785_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{n=q}^{\varvec{m}}\varvec{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="bold-italic">n</mi> <mo mathvariant="bold">=</mo> <mi mathvariant="bold-italic">q</mi> </mrow> <mrow> <mi mathvariant="bold-italic">m</mi> </mrow> </msup> <mrow> <mo mathvariant="bold">-</mo> <mn mathvariant="bold">1</mn> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We provide the first three largest odd coset leaders modulo <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_785_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{2n}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn mathvariant="bold">2</mn> <mi mathvariant="bold-italic">n</mi> </mrow> </math></EquationSource> </InlineEquation>. Sufficient and necessary conditions in terms of designed distance for negacyclic codes over <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_785_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textbf{GF}\varvec{(q)}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">GF</mi> <mrow> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">q</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of length <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_785_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{n=q}^{\varvec{m}}\varvec{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="bold-italic">n</mi> <mo mathvariant="bold">=</mo> <mi mathvariant="bold-italic">q</mi> </mrow> <mrow> <mi mathvariant="bold-italic">m</mi> </mrow> </msup> <mrow> <mo mathvariant="bold">-</mo> <mn mathvariant="bold">1</mn> </mrow> </mrow> </math></EquationSource> </InlineEquation> to be negacyclic dually-BCH codes are presented.</p>

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Negacyclic dually-BCH codes of length \(q^{m}-1\)

  • 期刊论文

  • 发表日期：

    2025年2月12日

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  • Ming Yu,
  • Xiaoshan Kai

摘要

In this paper, we investigate negacyclic dually-BCH codes over \(\textbf{GF}\varvec{(q)}\) GF ( q ) of length \(\varvec{n=q}^{\varvec{m}}\varvec{-1}\) n = q m - 1 . We provide the first three largest odd coset leaders modulo \(\varvec{2n}\) 2 n . Sufficient and necessary conditions in terms of designed distance for negacyclic codes over \(\textbf{GF}\varvec{(q)}\) GF ( q ) of length \(\varvec{n=q}^{\varvec{m}}\varvec{-1}\) n = q m - 1 to be negacyclic dually-BCH codes are presented.