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<p>This paper focuses on the study of triple-twisted generalized Reed–Solomon (TTGRS) codes over a finite field <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1595_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <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>, having twists <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1595_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="82" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{t} = (1, 2, 3)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi mathvariant="bold-italic">t</mi> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and hooks <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1595_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{h} = (0, 1, 2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi mathvariant="bold-italic">h</mi> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. We have obtained the necessary and sufficient conditions for such TTGRS codes to be MDS, AMDS, and AAMDS via algebraic techniques. We have also enumerated these codes for some particular values of the parameters. Moreover, we have presented some non-trivial examples for MDS, AMDS, and AAMDS TTGRS codes with various parameters. Further, we have studied the hulls of these codes, and under various conditions, obtained necessary and sufficient conditions for these codes to have a hull with dimensions varying from 0 to 5.</p>

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A class of triple-twisted GRS codes

  • 期刊论文

  • 发表日期：

    2025年3月5日

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  • Kapish Chand Meena,
  • Piyush Pachauri,
  • Ambrish Awasthi,
  • Maheshanand Bhaintwal

摘要

This paper focuses on the study of triple-twisted generalized Reed–Solomon (TTGRS) codes over a finite field \({\mathbb {F}}_q\) F q , having twists \(\varvec{t} = (1, 2, 3)\) t = ( 1 , 2 , 3 ) and hooks \(\varvec{h} = (0, 1, 2)\) h = ( 0 , 1 , 2 ) . We have obtained the necessary and sufficient conditions for such TTGRS codes to be MDS, AMDS, and AAMDS via algebraic techniques. We have also enumerated these codes for some particular values of the parameters. Moreover, we have presented some non-trivial examples for MDS, AMDS, and AAMDS TTGRS codes with various parameters. Further, we have studied the hulls of these codes, and under various conditions, obtained necessary and sufficient conditions for these codes to have a hull with dimensions varying from 0 to 5.