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- W2023454646 abstract "The Sphere-packing bound, Singleton bound, Wang-Xing-Safavi-Naini bound, Johnson bound, and Gilbert-Varshamov bound on the subspace codes<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:msub><mml:mrow><mml:mfenced separators=|><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi><mml:mo>,</mml:mo><mml:mo stretchy=false>(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>based on subspaces of type<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mo stretchy=false>(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:math>in singular linear space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant=double-struck>F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>over finite fields<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=double-struck>F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>are presented. Then, we prove that codes based on subspaces of type<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mo stretchy=false>(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:math>in singular linear space attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant=double-struck>F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>." @default.
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- W2023454646 date "2014-01-01" @default.
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- W2023454646 title "Bounds on Subspace Codes Based on Subspaces of Type(m,1)in Singular Linear Space" @default.
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