Novel q-ary Code Design for One Edit or Adjacent Transposition Error

Abstract

In this work, we delve into the typical errors that frequently arise in communication and storage systems, including deletion, insertion, substitution, and adjacent transposition errors. To effectively address these errors, a novel q-ary code construction (q ≥ 2) which consists of three constraints is proposed. Significantly, the devised codes mark the initial venture into q-ary code design, exhibiting 2 log q n + 4 redundancy symbols in rectifying a single deletion, insertion, substitution, or adjacent transposition error. This work also provides a meticulous mathematical analysis of the design of the proposed code, especially how our proposed code can distinguish the substitution and adjacent transposition error scenarios. In addition, a comprehensive decoding procedure for all error scenarios is also proposed.