Abstract

We investigate the density of codes in the complex Grassmann manifolds Gℂ n,p equipped with the chordal distance. The density of a code is defined as the fraction of the Grassmannian covered by ‘kissing’ balls of equal radius centered around the codewords. The kissing radius cannot be determined solely from the minimum distance, nonetheless upper and lower bounds as a function of minimum distance only are provided, along with the corresponding bounds on the density. This leads to a refinement of the Hamming bound for Grassmannian codes. Finally, we provide explicit bounds on code cardinality and minimum distance, notably a generalization of a bound on minimum distance previously proven only for line packing (p = 1).

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