Systems and Methods for Multi-Level Quasi-Cyclic Low Density Parity Check Codes

Various embodiments of the present invention provide systems and methods for generating a code format. One method discussed includes: Various embodiments of the present invention provide methods for generating a code format. Such methods include: receiving an indication of a low weight codeword having a trapping set; selecting an initial value for a base matrix; testing the low weight codeword after modification by the initial value to determine an updated weight of the low weight codeword; and testing the low weight codeword after modification by the initial value to determine whether the trapping set remains.