Optical Fiber Communications 4th Edition by Gerd Keiser

Exercise 20

In the (7,4) linear Hamming code the first four bits of a code word are the information bits b 1 , b 2 , b 3 , b 4 and the next three bits b 5 , b 6 , b 7 are the check bits, which are given by
b 5 = b 1 + b 3 + b 4
b 6 = b 1 + b 2 + b 4
b 7 = b 2 + b 3 + b 4
Make a table listing the sixteen possible 4-bit information words, that is, 0000 through 1111, and the corresponding 7-bit code words.