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<p>In this article, we introduce the sixth-order cyclotomy over <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4883_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {Z}_{2m},m\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="double-struck">Z</mi> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </msub> <mo>,</mo> <mi>m</mi> </mrow> </math></EquationSource> </InlineEquation> is a prime and develop dual-containing cyclic codes, along with their augmented codes, resulting in optimal cyclic codes. By utilizing these cyclic codes, we design quantum synchronizable codes (QSCs) and Calderbank–Shor–Steane (CSS) quantum codes. Additionally, we derive some new CSS quantum codes and also demonstrate that the obtained QSCs exhibit maximum tolerance to alignment errors.</p>

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Applications of order six cyclotomy to construct CSS quantum codes and quantum synchronizable codes

  • 期刊论文

  • 发表日期：

    2025年8月19日

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  • Pramod Kumar Kewat,
  • Varsha Tiwari

摘要

In this article, we introduce the sixth-order cyclotomy over \(\mathbb {Z}_{2m},m\) Z 2 m , m is a prime and develop dual-containing cyclic codes, along with their augmented codes, resulting in optimal cyclic codes. By utilizing these cyclic codes, we design quantum synchronizable codes (QSCs) and Calderbank–Shor–Steane (CSS) quantum codes. Additionally, we derive some new CSS quantum codes and also demonstrate that the obtained QSCs exhibit maximum tolerance to alignment errors.