Conservative Codes

NT(x) = 2. To find N(4, 2) we see that only 0010, 0100, 0110, 1001, 1011, and l l o l llave,2 1 NT(x) = t } l . This notation means that the information words wit,li t i , t?, . . . , and t, transitions are transformed to some k-bit vect.or wirh t transitions by complementing some even bits. One of t.he two check symbols in c will then be appended t.0 the right,end of the transformed word to obtain the fina.1 code xvorcl, a s depict,ed in fig. 1. The vector CO is appended if 21; = 0 a i d C has a negative sign or zk = 1 and C has a positive sign; otherwise, c1 is appended. This allows the creation of one (or zero) transition when C has a positive (or negative) sign. To obtain a conservative code, the final code word must have l ( k + ~ ) / 2 ] transitions; therefore, all maps must satisfy therefore, N(4,2) = 6. Definition Let = 21 , , . 2n be a binary vector, then let x[3] denote where the first j even bits are complemented; i.e. xLJ1 = z152z354”’z2j-152jzzjs1.~. z,. For instance, if x = 100