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Optimal (r, δ)-Locally Repairable Codes From Simplex Code and Cap Code
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DOI：10.1109/ACCESS.2020.3040320.png)
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Locally repairable codes (LRCs) are implemented in distributed storage systems (DSSs) due to their low repair overhead. A linear code C is said to have (r, delta)-locality if for each coordinate i, there exists a punctured subcode of C with support containing i, whose length is at most r + delta - 1 and whose minimum distance is at least delta. An LRC is called optimal if its minimum distance attains Singleton-type bound was proposed. In this letter, optimal LRCs are considered. We first determine (r, delta)-locality of three dimensional Simplex code, then using anticode strategy, a class of [3q, 3, 2q - 1](q) LRCs with (2, q) locality are derived for general q. Finally, using an ovoid in PG(3; q), we construct [q(2)+1, 4, q(q-1)](q) and [4q-4, 3q-5](q) LRCs with r = 3 and delta = q - 1. All LRCs constructed in this letter attain the Singleton-type bound.
Keyword:
Codecs
Generators
Spread spectrum communication
Linear codes
Maintenance engineering
Licenses
Interpolation
Singleton-type bound
simplex code
optimal locally repairable codes
cap code
期刊
IF:
3.6
论文数:
9.8W
被引数:
29.4W
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