Small-d MSR Codes With Optimal Access, Optimal Sub-Packetization, and Linear Field Size
نویسندگان
چکیده
This paper presents an explicit construction of a class optimal-access, minimum storage regenerating (MSR) codes, for small values the number $d$ helper nodes. The is valid any parameter set notation="LaTeX">$(n,k,d)$ with notation="LaTeX">$d \in \{k+1, k+2, k+3\}$ and employs finite field notation="LaTeX">$\mathbb {F}_{q}$ size notation="LaTeX">$q=O(n)$ . We will refer to constructed codes as notation="LaTeX">$\text {Small-}\mathsf {d}$ MSR codes. sub-packetization level notation="LaTeX">$\alpha $ given by = s^{{\lceil \frac {n}{s}\rceil }}$ , where notation="LaTeX">$s=d-k+1$ By earlier result on optimal-access this smallest value possible.
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Explicit MSR Codes with Optimal Access, Optimal Sub-Packetization and Small Field Size for $d = k+1, k+2, k+3$
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2023
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2023.3250458