Hamming-weight constrained coded arrays based on covering codes

We present a framework based on covering codes over the set of binary n-words for coding data into n × n binary arrays with a prescribed upper bound on the Hamming weight (i.e., number of 1´s) in each row and column. We obtain previously presented schemes for the case when the upper bound is n/2 as special cases of this framework and we study also another potentially practically relevant specialization when the underlying covering code is the first-order Reed-Muller code. Like the previous schemes for the n/2 case, the proposed framework and schemes may have applications in improving the performance of a next-generation memory based on programmable resistive devices arranged in a crossbar architecture.