The construction of some bit and byte error control codes using partial Steiner systems

A design-theoretic approach to binary linear codes that are single-error correcting (SEC) and double-error-detecting (DED) with the capability of detecting any error within a single byte of even width w (BED) is developed. A construction of SEC-BED-DED codes from ordinary binary linear codes utilizing partial Steiner systems is given. The construction produces some codes with higher rates than those known previously. The codes constructed may inherit special properties from the Steiner systems from which are derived. In particular, some rotational odd-weight-column codes are obtained