The Singleton Bound for Network Error-Correcting Codes

Inspired by network coding, network error-correcting codes was introduced in "N. Cai, R. W. Yeung, Network coding and error correction" for multicasting a source message to a set of nodes on a network. The usual approach in existing networks, namely link-by-link error correction, is a special case of network error correction. In "N. Cai, R. W. Yeung, Network coding and error correction", network generalizations of the Hamming bound and the Gilbert-Varshamov bound were obtained. In this paper, we prove the network generalizations of the Singleton Bound and its tightness.

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