<p>The fundamental problem of subspace coding is to explore the maximum possible cardinality <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_795_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="90" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{A}_{\varvec{q}}\varvec{(n, d, k)}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">A</mi> </mrow> <mrow> <mi mathvariant="bold-italic">q</mi> </mrow> </msub> <mrow> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">n</mi> <mo mathvariant="bold">,</mo> <mi mathvariant="bold-italic">d</mi> <mo mathvariant="bold">,</mo> <mi mathvariant="bold-italic">k</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of a set of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_795_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{k}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> </math></EquationSource> </InlineEquation>-dimensional subspaces of an <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_795_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">n</mi> </mrow> </math></EquationSource> </InlineEquation>-dimensional vector space over <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_795_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{\mathbb {F}_q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="double-struck">F</mi> <mi mathvariant="bold-italic">q</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> such that the subspace distance satisfies <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_795_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="137" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{d}_{\varvec{S}}\varvec{(W_1, W_2) \ge d}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">d</mi> </mrow> <mrow> <mi mathvariant="bold-italic">S</mi> </mrow> </msub> <mrow> <mo mathvariant="bold" stretchy="false">(</mo> <msub> <mi mathvariant="bold-italic">W</mi> <mn mathvariant="bold">1</mn> </msub> <mo mathvariant="bold">,</mo> <msub> <mi mathvariant="bold-italic">W</mi> <mn mathvariant="bold">2</mn> </msub> <mo mathvariant="bold" stretchy="false">)</mo> <mo mathvariant="bold">≥</mo> <mi mathvariant="bold-italic">d</mi> </mrow> </mrow> </math></EquationSource> </InlineEquation> for any two distinct subspaces <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_795_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{W}_{\varvec{1}}\varvec{,} \varvec{W}_{\varvec{2}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">W</mi> </mrow> <mrow> <mn mathvariant="bold">1</mn> </mrow> </msub> <mrow> <mo mathvariant="bold">,</mo> </mrow> <msub> <mrow> <mi mathvariant="bold-italic">W</mi> </mrow> <mrow> <mn mathvariant="bold">2</mn> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation> in this set. In this paper, we construct a new class of constant dimension codes (CDCs) by generalizing the coset construction and combining it with CDCs derived from parallel linkage construction and coset construction with an aim to improve the new lower bounds of <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_795_Article_IEq7.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="96" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{A}_{\varvec{q}}\varvec{(n, d, k).}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">A</mi> </mrow> <mrow> <mi mathvariant="bold-italic">q</mi> </mrow> </msub> <mrow> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">n</mi> <mo mathvariant="bold">,</mo> <mi mathvariant="bold-italic">d</mi> <mo mathvariant="bold">,</mo> <mi mathvariant="bold-italic">k</mi> <mo mathvariant="bold" stretchy="false">)</mo> <mo mathvariant="bold">.</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> We found a remarkable improvement in some of the lower bounds of <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_795_Article_IEq7.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="96" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{A}_{\varvec{q}}\varvec{(n, d, k).}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">A</mi> </mrow> <mrow> <mi mathvariant="bold-italic">q</mi> </mrow> </msub> <mrow> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">n</mi> <mo mathvariant="bold">,</mo> <mi mathvariant="bold-italic">d</mi> <mo mathvariant="bold">,</mo> <mi mathvariant="bold-italic">k</mi> <mo mathvariant="bold" stretchy="false">)</mo> <mo mathvariant="bold">.</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation></p>