Sparse and Balanced MDS Codes over Small Fields

11/11/2020

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by   Tingting Chen, et al.

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Maximum Distance Separable (MDS) codes with a sparse and balanced generator matrix are appealing in distributed storage systems for balancing and minimizing the computational load. Such codes have been constructed via Reed-Solomon codes over large fields. In this paper, we focus on small fields. We prove that there exists an [n,k]_q MDS code that has a sparse and balanced generator matrix for any q≥ n provided that n≤ 2k, by designing several algorithms with complexity running in polynomial time in k and n.