The all-optical linear array with a reconfigurable pipelined bus system (OLARPBS) optical conduit parallel computing model consists of pipelined optical conduits (buses) that interconnect all-optical processing elements. Previous work on the OLARPBS, following the designs of predecessor models, considered interconnections that mostly, rigidly connected a linear array of processing elements in the same specific order. Such rigidness results in a communication (memory) bound architecture and imposes algorithm scheduling difficulties, both of which potentially limit the capability of the model. A highly scalable and flexible interconnect, designed for high-bandwidth and high-speed interconnections, is developed in this paper. A matrix multiplication algorithm is designed to take advantage of this new interconnection design and includes a comparison with a previous algorithm. The advantages include addressing the communication limitations and enabling more flexible algorithms with increased processing efficiency.