  The two-sender unicast index coding problem is the most fundamental
multi-sender index coding problem. The two senders collectively cater to the
demands of all the receivers, by taking advantage of the knowledge of their
side-information. Each receiver demands a unique message and has some
side-information. Weakly secure index coding problem is a practical version of
the index coding problem in the presence of an eavesdropper. The eavesdropper
can not gain any information about the messages he does not have, by listening
to the senders' transmissions. We provide constructions of weakly secure linear
codes for different classes of the two-sender unicast index coding problem,
using those of its sub-problems. The constructions are valid only if such codes
exist for all the sub-problems under consideration. We identify some classes of
the two-sender problem, where the constructions provide optimal weakly secure
linear index codes.
