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<p>In this paper, we construct two interesting classes of LCD codes and double circulant LCD codes using self-dual bases and self-dual normal bases over the Galois ring <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3310_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="77" /> </InlineMediaObject> <EquationSource Format="TEX">\(GR(p^{r},m)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mi>R</mi> <mo stretchy="false">(</mo> <msup> <mi>p</mi> <mi>r</mi> </msup> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Then we provide a new class of LCD MRD generalized Gabidulin codes and show that they have good parameters.</p>

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LCD codes over Galois rings

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • F. Rebaine,
  • K. Guenda,
  • T. A. Gulliver

摘要

In this paper, we construct two interesting classes of LCD codes and double circulant LCD codes using self-dual bases and self-dual normal bases over the Galois ring \(GR(p^{r},m)\) G R ( p r , m ) . Then we provide a new class of LCD MRD generalized Gabidulin codes and show that they have good parameters.