Optimal Index Codes for a New Class of Interlinked Cycle Structure

The interlinked cycle (IC) structure that generalizes cycles and cliques was defined by Thapa, Ong, and Johnson. Interlinked-cycle-cover (ICC) scheme that leverages IC structures in digraphs to construct scalar linear index codes was proposed. A class of infinitely many digraphs, where the proposed scalar linear codes based on ICC scheme are optimal were characterized by Thapa et. al. In this paper, we provide an addition to this class by providing optimal length index codes for IC structures with one cycle among non-inner vertex set.