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The capacity of symmetric instance of the multiple unicast index codingproblem with neighboring antidotes (side-information) with number of messagesequal to the number of receivers was given by Maleki, Cadambe and Jafar. Inthis paper we consider ten symmetric multiple unicast problems with lesserantidotes than considered by them and explicitly construct scalar linear codesfor these problems. These codes are shown to achieve the capacity orequivalently these codes shown to be of optimal length. Also, the constructedcodes enable the receivers use small number of transmissions to decode theirwanted messages which is important to have the probability of message errorreduced in a noisy broadcast channel. Some of the cases considered are shown tobe critical index coding problems and these codes help to identify some of thesubclasses considered by others to be not critical index coding problems.

Optimal Scalar Linear Index Codes for Some Symmetric Multiple Unicast Problems