Optimal Weakly Secure Linear Codes for Some Classes of the Two-Sender\n Index Coding Problem

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