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<p>The hull of a linear code <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathcal {C}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">C</mi> </math></EquationSource> </InlineEquation> is the intersection of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathcal {C}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">C</mi> </math></EquationSource> </InlineEquation> with its dual code. We present and analyze the sequence of numbers of linear codes with increasing hull dimension but the same length <i>n</i> and dimension <i>k</i>. We also present classification results for binary and ternary linear codes with trivial hulls (LCD and self-orthogonal) for some values of the length <i>n</i> and dimension <i>k</i>, comparing the obtained numbers with the number of all linear codes for the same <i>n</i> and <i>k</i>.</p>

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Sequence of numbers of linear codes with increasing hull dimensions

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Stefka Bouyuklieva,
  • Iliya Bouyukliev,
  • Ferruh Özbudak

摘要

The hull of a linear code \({\mathcal {C}}\) C is the intersection of \({\mathcal {C}}\) C with its dual code. We present and analyze the sequence of numbers of linear codes with increasing hull dimension but the same length n and dimension k. We also present classification results for binary and ternary linear codes with trivial hulls (LCD and self-orthogonal) for some values of the length n and dimension k, comparing the obtained numbers with the number of all linear codes for the same n and k.