Ternary Golay code

<p>In <a href="/facts/Coding_theory/SBqStoGL">coding theory</a>, the ternary Golay codes are two closely related <a href="/facts/Error-correcting_code/cLUTUJrA">error-correcting codes</a>.
The code generally known simply as the ternary Golay code is an 
  
    
      
        [
        11
        ,
        6
        ,
        5
        
          ]
          
            3
          
        
      
    
    {\displaystyle [11,6,5]_{3}}
  
-code, that is, it is a <a href="/facts/Linear_code/HoFI3eyF">linear code</a> over a <a href="/facts/Ternary_numeral_system/bMUfR74P">ternary</a> alphabet; the <a href="/facts/Block_code/QVuqpGga">relative distance</a> of the code is as large as it possibly can be for a ternary code, and hence, the ternary Golay code is a <a href="/facts/Perfect_code/3P8HVgGF">perfect code</a>.
The extended ternary Golay code is a [12, 6, 6] <a href="/facts/Linear_code/HoFI3eyF">linear code</a> obtained by adding a zero-sum <a href="/facts/Check_digit/qMlumJpU">check digit</a> to the [11, 6, 5] code.
In finite <a href="/facts/Group_theory/NfowcI5H">group theory</a>, the extended ternary Golay code is sometimes referred to as the ternary Golay code.
</p>

Ternary Golay code open-in-new

Ternary Golay code