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• W2803724614 abstract "Up to now, many (k + r, k, N) minimum-storage regenerating (MSR) codes with k information nodes, r parity nodes, and node capacity N have been proposed. However, most of them are constructed over a relatively large finite field. In this paper, we propose three high-rate MSR codes over small finite fields. First, the new MSR code C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> with the optimal access property for all nodes is constructed over small finite field Fq, for example q = 3 for even r or q ≥ r + 1 for odd r, which is much smaller than that of the known one given by Ye and Barg. Further, considering to reduce the node capacity, another new MSR code C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> over F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>q</sub> with q ≥ r + 2 is generated based on C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> , which can effectively reduce the node capacity of C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> by a factor of r <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>r-1</sup> . However, only the first k nodes of C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> have the optimal access property. Therefore, the new MSR code C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>3</sub> over F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>q</sub> with q ≥ r + 2 which has the optimal access property for all nodes is proposed by modifying C2. Notably, in contrast to C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> , the node capacity of C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>3</sub> is decreased by a factor of r <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>r-2</sup> ." @default.
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• W2803724614 date "2018-01-01" @default.
• W2803724614 modified "2023-10-18" @default.
• W2803724614 title "Explicit Constructions of High-Rate MSR Codes with Optimal Access Property over Small Finite Fields" @default.
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• W2803724614 doi "https://doi.org/10.1109/tcomm.2018.2836445" @default.
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