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<p>In this paper, we completely determine the dimension of Hermitian hulls of Reed–Solomon codes for lengths <i>n</i> equal to the cardinality of the underlying finite field <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {F}_{q^2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <msup> <mi>q</mi> <mn>2</mn> </msup> </msub> </math></EquationSource> </InlineEquation> or to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, where <i>k</i> is the dimension of the Reed–Solomon code, by explicitly constructing a basis. We also determine, in some cases, whether Hermitian hulls of Reed–Solomon codes are generalized Reed–Solomon (GRS) codes. Consequently, we apply our results to construct MDS entanglement-assisted quantum error-correcting codes (EAQECCs).</p>

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Analysis of Hermitian hulls of Reed–Solomon codes and EAQECCs

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Hailong Xu,
  • Qi Liu,
  • Haiyan Zhou

摘要

In this paper, we completely determine the dimension of Hermitian hulls of Reed–Solomon codes for lengths n equal to the cardinality of the underlying finite field \(\mathbb {F}_{q^2}\) F q 2 or to \(k+1\) k + 1 , where k is the dimension of the Reed–Solomon code, by explicitly constructing a basis. We also determine, in some cases, whether Hermitian hulls of Reed–Solomon codes are generalized Reed–Solomon (GRS) codes. Consequently, we apply our results to construct MDS entanglement-assisted quantum error-correcting codes (EAQECCs).