Let p be any prime number such that <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1600_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="106" /> </InlineMediaObject> <EquationSource Format="TEX">$p\equiv 1 \pmod 4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>≡</mo> <mn>1</mn> <mspace width="4.44443pt" /> <mo stretchy="false">(</mo> <mo>mod</mo> <mspace width="0.277778em" /> <mn>4</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, and let <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1600_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {F}}_p$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> be the finite field of p elements. In this paper, we first construct a new AMDS symbol-pair cyclic code of length 4p and of symbol-pair distance 9 by examining its generator polynomial. We then use the generator polynomial to obtain a family of <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1600_Article_IEq7.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">$(p-1)/2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> AMDS symbol-pair constacyclic codes of the same length and of the same symbol-pair distance.

A new family of AMDS symbol-pair constacyclic codes of length $\textbf{4p}$ and symbol-pair distance $\textbf{9}$

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发表日期：

2025年2月27日

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Hai Q. Dinh,
Hieu V. Ha,
Bac T. Nguyen,
Thieu N. Vo

摘要

Let p be any prime number such that $p\equiv 1 \pmod 4$ $p \equiv 1 (mod 4)$ , and let ${\mathbb {F}}_p$ $F_{p}$ be the finite field of p elements. In this paper, we first construct a new AMDS symbol-pair cyclic code of length 4p and of symbol-pair distance 9 by examining its generator polynomial. We then use the generator polynomial to obtain a family of $(p-1)/2$ $(p - 1) / 2$ AMDS symbol-pair constacyclic codes of the same length and of the same symbol-pair distance.

A new family of AMDS symbol-pair constacyclic codes of length \(\textbf{4p}\) and symbol-pair distance \(\textbf{9}\)

摘要