Sparse and Balanced MDS Codes Over Small Fields
نویسندگان
چکیده
Maximum Distance Separable (MDS) codes with a sparse and balanced generator matrix are appealing in distributed storage systems for balancing minimizing the computational load. Such have been constructed via Reed-Solomon over large fields. In this paper, we focus on small We prove that there exists an $[n,k]_{q}$ MDS code has any notation="LaTeX">$q\geq n-1$ provided notation="LaTeX">$n\leq 2k$ , by designing several algorithms complexity running polynomial time notation="LaTeX">$k$ notation="LaTeX">$n$ . For case notation="LaTeX">$n>2k$ give some constructions notation="LaTeX">$q=n=p^{s}$ notation="LaTeX">$k=p^{e}m$ based sumsets, when notation="LaTeX">$e\leq s-2$ notation="LaTeX">$m\leq p-1$ or notation="LaTeX">$e=s-1$ notation="LaTeX">$m < \frac {p}{2}$
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2022
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2022.3162524