Bounds on the asymptotic rate of binary constant subblock-composition codes

The study of binary constant subblock-composition codes (CSCCs) has recently gained attention due to their application in diverse fields. These codes are a class of constrained codes where each codeword is partitioned into equal sized subblocks, and every subblock has the same fixed weight. We present novel upper and lower bounds on the asymptotic rate for binary CSCCs, using the sphere-packing and Gilbert-Varshamov (GV) type bounds, respectively. For a fixed subblock length and small code distance, we show that the asymptotic rate for CSCCs is strictly lower than the corresponding rate for constant weight codes (CWCs). We also provide a correction to an earlier result by Chee et al. (2014) on the asymptotic CSCC rate.