Bounds on Subspace Codes Based on Subspaces of Type (m, 1) in Singular Linear Space

The Sphere-packing bound, Singleton bound, Wang-Xing-Safavi-Naini bound, Johnson bound, and Gilbert-Varshamov bound on the subspace codes based on subspaces of type in singular linear space over finite fields are presented. Then, we prove that codes based on subspaces of type in singular linear space attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures in .

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