Detecting Substitutions and Transpositions of Characters

Substitution errors, where individual characters are altered, and transposition errors, where two consecutive characters are interchanged, are commonly caused by human operators. In this paper, codes that detect a single substitution error or a single transposition error are studied. In particular, it is shown that such codes of length n over an alphabet of q characters have at most qn−1 codewords if q ≥ 3 and at most d2n/3e codewords if q = 2. Codes which have that many codewords are called optimal codes. We present optimal codes for all values of n and q. Simple encoding techniques for these codes are also described.