Locally recoverable code: Difference between revisions

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|doi= 10.1007/s10623-022-01046-y

|publisher=IEEE

|arxiv=2104.01434

}}</ref><ref>{{Citation

|first1=K.

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It is well-known that LRC is a [[linear code|code]] that needs only a limited [[Set (mathematics)|set]] of other symbols to be accessed in order to restore every symbol in a codeword. This idea is very important for distributed and [[cloud storage]] systems since the most common error case is when one storage node fails (erasure). The main objective is to recover as much [[data]] as possible from the fewest additional storage nodes in order to restore the node. Hence, Locally Recoverable Codes are crucial for such systems.

The following [[definition]] of the LRC follows from the description above: an <math>[n, k, r]</math>-Locally Recoverable Code (LRC code) of length <math>n</math> is a [[linear code|code]] that produces an <math>n</math>-symbol codeword from <math>k</math> information symbols, and for any symbol of the codeword, there exist at most <math>r</math> other symbols such that the value of the symbol can be recovered from them. The locality [[parameter]] satisfies <math>1 \leq r \leq k</math> because the entire codeword can be found by accessing <math>k</math> symbols other than the erased symbol. Furthermore, Locally Recoverable Codes, having the minimum [[Hamming distance|distance]] <math>d</math>, can recover <math>d-1</math> erasures.

==Definition==

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{{reflist}}

[[Category:Cryptography]]

[[Category:Information theory]]

[[Category:Mathematics]] [[Category:Cryptography]] [[Category:Information theory]] [[Category:Error detection and correction]]