In the maximum-likelihood decoding under a non-Gaussian noise, the decoding region is bounded by complex curves instead of a perpendicular bisector corresponding to the Gaussian noise. Therefore, the error rate is not evaluated by the Euclidean distance. The Bhattacharyya distance is adopted since it can evaluate the error performance for a noise with an arbitrary distribution. Upper bound formulae of a bit error rate and an event error rate are obtained based on the error-weight-profile method proposed by Zehavi and Wolf. The method is modified for a non-Gaussian channel by using the Bhattacharyya distance instead of the Euclidean distance. To determine the optimum code for an impulsive noise channel, the upper bound of the bit error rate is calculated for each code having an encoder with given shift-register lehgth. The best code is selected as that having the minimum upper bound of the bit error rate. This method needs much computation time especially for a code with a long shift-register. To lighten the computation burden, a suboptimum search is also attempted. For an impulsive noise, modeled from an observation in digital subscriber loops, an optimum or suboptimum code is searched for among codes having encoders with a shift-register of up to 4 bits. By using a code with a 4-bit encoder, a coding gain of 20 dB is obtained at the bit error rate 10-5. It is 11 dB more than that obtained by Ungerboeck's code.