Golay Code Implementation – Detecting Errors
It is easy to detect errors in a codeword.
• Using the parity bit to check for odd numbers of errors
If parity is correct
• Computing the 23-bit syndrome of the codeword and check for zero
The syndrome is the reminder left after the codeword is divided by the polynomial, modulo-2. It is equal to zero if the Golay code is valid, else non-zero.
A hand computation example is shown below using the previous 686555h, bit reversed for the division process.¶

101011100011  10101010101001100001011  ( AE3h then 555h then checkbits)                        
                   101011100011 (checkbits)                                    
                   ------------  <---------- Exclusive-OR                                     
                        100100101100                                
                        101011100011                                
                        ------------                                
                          111100111100                              
                          101011100011                              
                          ------------                              
                           101110111111                             
                           101011100011                             
                           ------------                             
                              101011100011                          
                              101011100011                          
                              ------------                          
                              000000000000 <-- syndrome = 0