The claimed embodiments provide methods, apparatuses and systems directed to run-length limited (RLL) coding of data. In one implementation, concatenatable RLL codes with run lengths of zeroes not exceeding k are constructed for any rate N/(N+1) where N.ltoreq.2.sup.k-2+k-1. As code rates increase, the value of k departs from the minimum possible value more slowly than that of many other codes. Further, occurrences of k-bit run lengths occur only at the juncture of two codewords. Due to this, the codes are mostly k-1. This quality makes the codes ideal for parity bit insertion applications such as LDPC channels. The method, in one implementation, places the bit addresses of violating sequences in a table at the beginning of the codeword, and the user data, occupying the locations where the table entries are placed, are moved into the locations of the violating sequences. This is done iteratively and in a way which provides for cases in which the violating sequence is inside the address table itself.