Optimal vector linear index codes for some symmetric side information problems

This paper deals with vector linear index codes for multiple unicast index coding problems where there is a source with K messages and there are K receivers each wanting a unique message and having symmetric (with respect to the receiver index) two-sided antidotes (side information). Starting from a given multiple unicast index coding problem with K messages and symmetric one-sided antidotes for which a scalar linear index code ℭ is known, we give a construction procedure which constructs a sequence (indexed by m) of multiple unicast index coding problems with symmetric two-sided antidotes (for the same source) for all of which a vector linear code ℭ(m) is obtained from ℭ. Also, it is shown that if ℭ is optimal then ℭ(m) is also optimal for all m. To our knowledge, this is the first paper which gives a method to construct a sequence of optimal vector linear index codes