Sparse and Balanced MDS Codes over Small Fields

Tingting Chen; Xiande Zhang

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arXiv · 2011.05634

Sparse and Balanced MDS Codes over Small Fields

Tingting Chen·Xiande Zhang

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Abstract

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 $q\geq n$ provided that $n\leq 2k$, by designing several algorithms with complexity running in polynomial time in $k$ and $n$.

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Tingting Chen, Xiande Zhang. 2020-11-11. Sparse and Balanced MDS Codes over Small Fields. https://arxiv.org/abs/2011.05634

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