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The Computer Journal 1998 41(4):270-277; doi:10.1093/comjnl/41.4.270
© 1998 by British Computer Society
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Detecting Substitutions and Transpositions of Characters

K. A. S. Abdel-Ghaffar

Department of Electrical and Computer Engineering, University of California, Davis, CA 95616, USA Email: ghaffar{at}ece.ucdavis.edu

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 [2n/3] 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.

Received October 22, 1997. revised May 11, 1998.


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