Binary index codes using l-th NMDS codes

A procedure to obtain index codes for a given index coding problem by using l-th Near Maximum Distance Separable Codes (NMDS) codes is presented. The advantage of using l-th NMDS codes is the reduction in field size required. A trade off between field size and length of index codes is observed. Using appropriate l-th NMDS codes binary index codes for the index coding problem can be constructed. The index codes obtained through this technique make use of only the minimum value of cardinality of the side-information available at the receivers and do not use messages in their side-information. The index codes obtained through this technique are optimal for, but not limited to, special cases of index coding problems discussed in the paper. Finding an optimal solution of a general index coding problem is NP Hard and this technique helps in finding binary suboptimal solutions. Using the Gilbert-Varshamov bound, an upper bound on the length of optimal binary index codes is obtained. Specifically we obtain a length for which a binary index code is guaranteed to exist.