Locally recoverable code: Difference between revisions

Revision as of 21:43, 4 November 2024

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{{Short description|Coding Theory}}

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'''Locally Recoverable Codes''' are a family of [[Errorerror correction code|error correction codes]]s that were introduced first by D. S. Papailiopoulos and A. G. Dimakis<ref>{{Citation

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'''Locally Recoverable Codes''' are a family of [[Error correction code|error correction codes]] that were introduced first by D. S. Papailiopoulos and A. G. Dimakis<ref>{{Citation

|first1=Dimitris S.|last1=Papailiopoulos |first2=Alexandros G. |last2=Dimakis |title="Locally Repairable Codes" |chapter=Locally repairable codes |pages=2771–2775 |___location=Cambridge, MA, USA |publisher=IEEE International Symposium on Information Theory |date=2012 |doi=10.1109/ISIT.2012.6284027|isbn=978-1-4673-2579-0 }}</ref> and have been widely studied in [[Information theory]] due to their applications related to Distributive and Cloud Storage Systems.

<ref>{{Citation

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=== Tamo--Barg Construction ===

The Tamo--BargTamo—Barg construction utilizes good polynomials.<ref>{{Citation

|first1=I.|last1=Tamo |first2=A. |last2=Barg |title="A family of optimal locally recoverable code" |chapter=A family of optimal locally recoverable codes |pages=686–690 |___location=Honolulu, HI, USA |publisher=IEEE International Symposium on Information Theory |date=2014 |doi=10.1109/ISIT.2014.6874920|isbn=978-1-4799-5186-4 }}</ref>

:• Suppose that a <math>(r, \ell)</math>-good polynomial <math>f(x)</math> over <math>\mathbb F_{q}</math> is given with splitting covering <math>i \in \{1, \ldots, \ell\}</math>.