sentences:  The binary lexicographic codes are linear codes, and include the Hamming codes and the binary Golay codes.A lexicode of minimum distance "d" and length "n" over a finite field is generated by starting with the all-zero vector and iteratively adding the next vector (in lexicographic order) of minimum Hamming distance "d" from the vectors added so far.As an example, the length-3 lexicode of minimum distance 2 would consist of the vectors marked by an "X" in the following example