Tallini and Bose defined a random walk function on which an efficient encoding/decoding algorithm for second-order spectral-null (2-OSN) codes was based. Later, Yang enhanced Tallini-Bose code by using quasi 2-OSN codes. Both 2-OSN codes encode the information word into a balanced word and then append extra bits to make the length of this balanced word equal to 0 (or 2) modulo 4. The main innovation is to eliminate the need for appended bits, thereby increasing the code rate.