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Parallel architectures involves parallel communication with the aim of fast receiving of complete information with higher information rate at each nodes. To reduce the complexity of parallel communication we have considered Multi-Mesh of Trees (MMT) architecture for parallel communication and implemented Linear Network Coding (LNC) on MMT by proposing Linear-Code Multicast with Parallel Algorithms (LCM-PA) to achieve max-flow from the source to each receiving nodes. We wish to minimize the communication steps and time complexity involved in transfer of data from processor to processor during parallel communication while achieving the desired throughput in a multicast scenario. We developed a novel distributed parallel network approach, which is enriched by linear coding.