linear index coding scheme based on rank minimization over finite fields was introduced in [@ICSI] and random index coding was studied for infinitely long message length [@RI].

In addition to researches on the index coding schemes, relevance to other problems has been researched such as the equivalence between network coding and index coding, topological interference management, and duality with distributed storage systems [@EQU], [@TIM], [@DSS]. There are also many researches on variations of index coding instances. For example, erroneous broadcast channels were considered in [@SECIC] and coded side information was studied in [@BCSI], [@ICCSI]. Moreover, blind index coding instances where a sender only knows the probability distribution of side information were researched [@BlindIC] and functional index coding instances were introduced in [@FIC]. In contrast to conventional assumptions on side information, an index code in which side information errors exist, called an index code with side information errors (ICSIE) was studied in [@ICSIE].

Among these researches, we focus on an equivalence between network coding and index coding [@EQU] in which their equivalence was introduced and a corresponding index coding instance was derived for a given network coding instance. It was also shown that any network codes can be converted to the 