nodes through links and internal nodes. In order to improve the throughput gain, some internal nodes encode their incoming symbols, which is called network coding. In [@linearnetworkcode], it was proved that a linear network code for multicast in a network can achieve the max-flow bound. For multicast cases, there exist some algorithms to construct network codes achieving the maxflow-mincut capacity for a single source [@networkalgorithm1], [@networkalgorithm2].

In contrast to an error-free link case, a network code dealing with erroneous data on links was also studied, referred to as a network code with link errors (NCLE) in this paper. As erroneous data on links in a network are considered, the number of overall link errors in a network which network codes can overcome was studied [@networkerror1], [@networkerror2].

Index coding was introduced in [@Informed] for satellite communication systems which consist of one sender and several receivers. A sender has to transmit messages to receivers through a broadcast channel and receivers want to receive some messages and also know some messages priory as side information. Owing to its applications and relevance to other problems, index coding has attracted significant attention and various index coding schemes have accordingly been researched. For example, the optimal 