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<p>Subspace codes have attracted much attention in recent decades because of their applications in random network coding. Among these, cyclic subspace codes can be encoded and decoded more efficiently due to their special algebraic structure, attracting a great deal of scholarly research in recent years. In this paper, we present a family of cyclic subspace codes with minimum distance <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2k-2\)</EquationSource> </InlineEquation> and size <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((q-1+r)(q^{k}-1)^{r}(q^{n}-1)\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(n=(2r+1)k\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(r\ge 4\)</EquationSource> </InlineEquation>. In the case of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(n=(2r+1)k\)</EquationSource> </InlineEquation> with <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(4\le r&lt;q^{k}-1\)</EquationSource> </InlineEquation>, our codes have larger sizes than the known ones in the literature.</p>

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New construction of cyclic subspace codes via Sidon spaces

  • 期刊论文

  • 发表日期：

    2026年2月11日

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  • Shuhui Yu,
  • Lijun Ji

摘要

Subspace codes have attracted much attention in recent decades because of their applications in random network coding. Among these, cyclic subspace codes can be encoded and decoded more efficiently due to their special algebraic structure, attracting a great deal of scholarly research in recent years. In this paper, we present a family of cyclic subspace codes with minimum distance \(2k-2\) and size \((q-1+r)(q^{k}-1)^{r}(q^{n}-1)\) , where \(n=(2r+1)k\) and \(r\ge 4\) . In the case of \(n=(2r+1)k\) with \(4\le r<q^{k}-1\) , our codes have larger sizes than the known ones in the literature.