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<p>In this paper, we study the complementary dual subspace codes in more general setting (which are called <i>s</i>-Galois LCD subspace codes) by a uniform method. A necessary and sufficient condition for subspace codes to be <i>s</i>-Galois LCD subspace codes is determined. Using this condition, we give a sufficient condition under which a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1707_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda -\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>constacyclic subspace code is a <i>s</i>-Galois LCD subspace code. To enrich the <i>s</i>-Galois LCD subspace codes, by means of the matrix codes and matrix-product codes, we construct <i>s</i>-Galois LCD subspace codes.</p>

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Galois LCD subspace codes

  • 期刊论文

  • 发表日期：

    2025年8月7日

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  • Jie Liu,
  • Peng Hu,
  • Xiusheng Liu

摘要

In this paper, we study the complementary dual subspace codes in more general setting (which are called s-Galois LCD subspace codes) by a uniform method. A necessary and sufficient condition for subspace codes to be s-Galois LCD subspace codes is determined. Using this condition, we give a sufficient condition under which a \(\lambda -\) λ - constacyclic subspace code is a s-Galois LCD subspace code. To enrich the s-Galois LCD subspace codes, by means of the matrix codes and matrix-product codes, we construct s-Galois LCD subspace codes.