Locally recoverable code

<p>Locally recoverable codes are a family of <a href="/facts/Error_correction_code/cLUTUJrA">error correction codes</a> that were introduced first by D. S. Papailiopoulos and A. G. Dimakis and have been widely studied in <a href="/facts/Information_theory/qNLH3U5P">information theory</a> due to their applications related to distributive and <a href="/facts/Cloud_storage/cNw9IK3Q">cloud storage</a> systems.
</p><p>An 
  
    
      
        [
        n
        ,
        k
        ,
        d
        ,
        r
        
          ]
          
            q
          
        
      
    
    {\displaystyle [n,k,d,r]_{q}}
  
 LRC is an 
  
    
      
        [
        n
        ,
        k
        ,
        d
        
          ]
          
            q
          
        
      
    
    {\displaystyle [n,k,d]_{q}}
  
 <a href="/facts/Linear_code/HoFI3eyF">linear code</a> such that there is a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> 
  
    
      
        
          f
          
            i
          
        
      
    
    {\displaystyle f_{i}}
  
 that takes as input 
  
    
      
        i
      
    
    {\displaystyle i}
  
 and a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> of 
  
    
      
        r
      
    
    {\displaystyle r}
  
 other <a href="/facts/Coordinate_system/Mtd0q4SP">coordinates</a> of a codeword 
  
    
      
        c
        =
        (
        
          c
          
            1
          
        
        ,
        …
        ,
        
          c
          
            n
          
        
        )
        ∈
        C
      
    
    {\displaystyle c=(c_{1},\ldots ,c_{n})\in C}
  
 different from 
  
    
      
        
          c
          
            i
          
        
      
    
    {\displaystyle c_{i}}
  
, and outputs 
  
    
      
        
          c
          
            i
          
        
      
    
    {\displaystyle c_{i}}
  
.
</p>

Locally recoverable code open-in-new

Locally recoverable code