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<p>In this article, we investigate all almost maximum distance separable (briefly, AMDS) constacyclic codes over the finite field <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\({\mathbb {F}}_{p^m}\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(p&gt;3\)</EquationSource> </InlineEquation> is an odd prime. In addition, we explore the construction of quantum AMDS (qAMDS) codes using both Calderbank-Shor-Steane (CSS) and Hermitian constructions. These newly constructed codes possess different parameters compared to previous constructions.</p>

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Amds codes and quantum AMDS codes of length \(3p^s\) over \({\mathbb {F}}_{p^m}\)

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Hai Q. Dinh,
  • Bac T. Nguyen,
  • Hiep L. Thi

摘要

In this article, we investigate all almost maximum distance separable (briefly, AMDS) constacyclic codes over the finite field \({\mathbb {F}}_{p^m}\) , where \(p>3\) is an odd prime. In addition, we explore the construction of quantum AMDS (qAMDS) codes using both Calderbank-Shor-Steane (CSS) and Hermitian constructions. These newly constructed codes possess different parameters compared to previous constructions.