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On the Mathematical Theory of Error-Correcting Codes

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2 Author(s)

Hamming considered the problem of efficient, faultless transmission of binary data over a noisy channel. For a channel which corrupts no more than one binary digit in each sequence of length n, he constructed alphabets, the so-called Hamming codes, which permit error-free signalling. The authors study the analogous problem for channels which can corrupt a greater number of digits. Non-binary channels are also studied, and analogues of the Hamming codes are constructed. It is perhaps of interest that some of the techniques employed derive from algebraic and analytic number theory, mathematical disciplines not generally associated with the type of applied problems considered in this paper.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

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IBM Journal of Research and Development  (Volume:3 ,  Issue: 1 )