A class of binary signaling alphabets called “group alphabets” is described. The alphabets are generalizations of Hamming's error correcting codes and possess the following special features: (1) all letters are treated alike in transmission; (2) the encoding is simple to instrument; (3) maximum likelihood detection is relatively simple to instrument; and (4) in certain practical cases there exist no better alphabets. A compilation is given of group alphabets of length equal to or less than 10 binary digits.
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D. Slepian (1956) studied this question.
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