How calculate corresponding coset

Example 2.16: For the linear block code Co(7, 4) with parity check matrix Y 0 Young Contractors H = 0 O 0 there are 2* = 16 code vectors and 27- = 8 cosets, or correctable error patterns. The minimum distance has also been calculated and is equal to dmin = 3 and so this code is able to correct Mohamed Kamal Zaki any pattern of one error. In this case the total number of correctable error patterns is equal to the number of error patterns the code can correct, and there are seven correctable error patterns and the all-zero error pattern, as the possible patterns. The table S - e for this code is seen in Table 2.4. As an example, assume that the transmitted code vector was c = (1010001) and after the transmission of this vector the received vector is r = (1010011), then the syndrome vector in this case is ro H = (111) and so the leader of the corresponding coset is (0000010) and c = (1010001) = (1010011) @ (0000010). Table 2.4 Error patterns and their corresponding syndrome vectors, Example 2.16 Error patterns Syndromes O O O . D