A data storage system includes a memory circuit that has memory cells and a control circuit that is operable to receive data bits provided for storage in the memory cells. The control circuit is operable to receive a first matrix. Each row of the first matrix corresponds to a unique one of the data bits. The control circuit is operable to generate a second matrix having only the rows of the first matrix that correspond to the data bits provided for storage in a subset of the memory cells having stuck-at faults. The control circuit is operable to generate a third matrix having linearly independent columns of the second matrix. The control circuit is operable to encode the data bits to generate encoded data bits and redundant bits using the third matrix.