Packing and Covering Properties of CDCs and Subspace Codes

Constant-dimension codes (CDCs) and subspace codes have be en proposed for error control in network coding. In this paper, we first study the covering pro perties of CDCs. We derive bounds on the minimum cardinality of a CDC with a given covering radius and determine the asymptotic rate of optimal covering CDCs. We then study the packing and coverin g properties of subspace codes, which can be used with the subspace metric or the so-called modified subspace metric. We derive bounds on the cardinalities of packing and covering subspace codes, and w e etermine the maximum asymptotic rate of both packing and covering subspace codes for both the subs pace metric and the modified subspace metric.

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