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<p>In this paper, we exhibit an effective method for constructing entanglement-assisted quantum error-correcting (EAQEC) codes via Euclidean hulls of matrix product codes with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4899_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(t_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>t</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-partitioned Euclidean orthogonal property as the defining matrices over the finite fields. By this method, we obtain numerous new EAQEC codes, all of them have higher rate than current EAQEC codes available. Moreover, the dimensions, minimum distances and the number <i>c</i> of pre-shared maximally entangled states of our EAQEC codes are easily calculated and very flexible.</p>

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The Euclidean hulls of matrix product codes and their applications to EAQEC codes

  • 期刊论文

  • 发表日期：

    2025年8月20日

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  • Jie Liu,
  • Peng Hu,
  • Xiusheng Liu

摘要

In this paper, we exhibit an effective method for constructing entanglement-assisted quantum error-correcting (EAQEC) codes via Euclidean hulls of matrix product codes with \(t_1\) t 1 -partitioned Euclidean orthogonal property as the defining matrices over the finite fields. By this method, we obtain numerous new EAQEC codes, all of them have higher rate than current EAQEC codes available. Moreover, the dimensions, minimum distances and the number c of pre-shared maximally entangled states of our EAQEC codes are easily calculated and very flexible.