We investigate the error detection ability of intermediate nodes of zig-zag network with small downstream link. We show that the error detection capability of zig-zag networks in the presence of z malicious edges and 2z-1 limited links from node B to node u. Also, at last we analyze a family of networks, which shows that the upper bound of network is smaller than the bound we expected, indicating that Singleton bound is not the tightest bound in the particular condition of network. According to this result, we design corresponding encode and decode strategy to reach the bound we propose in this paper.
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