Construction of Linear Network Codes That Achieve a Rened Singleton Bound
The network error correction problem study is to extend classical error correction coding theory to a general network setting. In Cai and Yeung, network generalizations of the Hamming bound, the Singleton bound, and the Gilbert-Varshamov bound in classical algebraic coding theory were obtained. In particular, the tightness of the Singleton bound is preserved. The minimum rank for linear network codes, which plays a role similar to that of the minimum distance in decoding classical error-correcting codes, was introduced by Zhang. In this paper, the authors present a refined version of the Singleton bound for network error correction, and propose an algorithm for constructing network codes that achieve this bound.