Abstract
Summary form only given. At low signal-to-noise ratio, the geometric structure of a code is more important and more complicated than at high signal-to-noise ratio. Each codeword has an associated probability P i which is related to the probability that this particular codeword is the first incorrect decoding of the zero codeword with additive white Gaussian noise. The authors have found (among other things) an expression for the probability P c of correct decoding of a codeword in terms of the number of codewords, the Hamming weight, and P i .