Bounds and constructions for runlength-limited error-control block codes

摘要

Block codes satisfying (d,k) constraints are studied. These runlength-limited codes are useful for strong data in magnetic recording devices. Since most devices are noisy, the codes are often required to have some error-control capability. The authors consider codes that can detect or correct symmetric, asymmetric, or bit-shift errors. Explicit construction methods for error-detecting codes are presented. Upper bounds on the sizes of error-correcting codes based on sphere packing arguments are derived. The construction methods and the upper bounds improve upon the best known results concerning optimal runlength-limited error-control block codes.