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On decoding linear error-correcting codes--I

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1 Author(s)

A technique is described for finding simply computable numerical-valued functions of a received binary word whose value indicates where errors in transmission have occurred. Although it seems that a certain condition must usually be fulfilled for such functions to exist, or for our method to constitute an efficient procedure for finding them, there is, on the one hand, a strong tendency for "good" codes to satisfy the condition, while, on the other, it appears to be straightforward to construct codes which are good for a specified channel and also fulfill the condition. An advantage of the resulting decoding procedure is that it corrects and detects all possible errors; more precisely, if a word u is received and the coset \bar{u} to which u belongs has a unique leader e , the procedure concludes that u + e was sent, while if u has no unique leader, that fact, along with the weight of \bar{u} (and sometimes a little more) can be indicated. The ideas and techniques are illustrated by the construction of decoding procedures for the perfect (23, 12) three-error-correcting code.

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Information Theory, IRE Transactions on  (Volume:6 ,  Issue: 4 )