1. A method for transforming a generalized parity check matrix representing a linear block binary code, comprising: defining an input generalized parity check matrix for the linear block binary code; forming auxiliary sets from the input generalized parity check matrix; ordering subsets of each auxiliary set in a list; constructing parity check equations from the list of ordered subsets; translating the parity check equations into an output generalized parity check matrix; and decoding a message encoded according to the linear block binary code with the output generalized parity check matrix.