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The study of subblock-constrained codes has recently gained attention due totheir application in diverse fields. We present bounds on the size andasymptotic rate for two classes of subblock-constrained codes. The first classis binary constant subblock-composition codes (CSCCs), where each codeword ispartitioned into equal sized subblocks, and every subblock has the same fixedweight. The second class is binary subblock energy-constrained codes (SECCs),where the weight of every subblock exceeds a given threshold. We present novelupper and lower bounds on the code sizes and asymptotic rates for binary CSCCsand SECCs. For a fixed subblock length and small relative distance, we showthat the asymptotic rate for CSCCs (resp. SECCs) is strictly lower than thecorresponding rate for constant weight codes (CWCs) (resp. heavy weight codes(HWCs)). Further, for codes with high weight and low relative distance, we showthat the asymptotic rates for CSCCs is strictly lower than that of SECCs, whichcontrasts that the asymptotic rate for CWCs is equal to that of HWCs. We alsoprovide a correction to an earlier result by Chee et al. (2014) on theasymptotic CSCC rate. Additionally, we present several numerical examplescomparing the rates for CSCCs and SECCs with those for constant weight codesand heavy weight codes.

Bounds on the Size and Asymptotic Rate of Subblock-Constrained Codes