Group code

<p>In <a href="/facts/Coding_theory/SBqStoGL">coding theory</a>, group codes are a type of <a href="/facts/Coding_theory/SBqStoGL">code</a>. Group codes consist of

n
      
    
    {\displaystyle n}
  
 <a href="/facts/Linear_block_codes/HoFI3eyF">linear block codes</a> which are subgroups of 
  
    
      
        
          G
          
            n
          
        
      
    
    {\displaystyle G^{n}}
  
, where 
  
    
      
        G
      
    
    {\displaystyle G}
  
 is a finite <a href="/facts/Abelian_group/FfWwmx4R">Abelian group</a>.
</p><p>A systematic group code 
  
    
      
        C
      
    
    {\displaystyle C}
  
 is a code over 
  
    
      
        
          G
          
            n
          
        
      
    
    {\displaystyle G^{n}}
  
 of order 
  
    
      
        
          
            |
            G
            |
          
          
            k
          
        
      
    
    {\displaystyle \left|G\right|^{k}}
  
 defined by 
  
    
      
        n
        −
        k
      
    
    {\displaystyle n-k}
  
 <a href="/facts/Homomorphism/0gyqdEse">homomorphisms</a> which determine the <a href="/facts/Parity_check/peFp3Wau">parity check</a> bits. The remaining 
  
    
      
        k
      
    
    {\displaystyle k}
  
 bits are the information bits themselves.
</p>

Group code open-in-new

Group code