Various embodiments of the present invention provide systems and methods for encoding data. As an example, a data encoding circuit is disclosed that includes a first stage data encoder circuit and a second stage data encoder circuit. The first stage data encoder circuit is operable to provide a first stage output. The first stage data encoder circuit includes a first vector multiplier circuit operable to receive a data input and to multiply the data input by a first sparse matrix to yield a first interim value. The second stage encoder circuit includes a second vector multiplier circuit operable to multiply the first stage output by a second sparse matrix to yield a second interim value.