| Summary: | 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 <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ary code construction <inline-formula> <tex-math notation="LaTeX">$(q\geq 2)$ </tex-math></inline-formula> which consists of three constraints is proposed. Significantly, the devised codes mark the initial venture into <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ary code design, exhibiting <inline-formula> <tex-math notation="LaTeX">$2\log _{q} n +4$ </tex-math></inline-formula> 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.
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