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A new method using an error correcting code to reduce the probability of detection error for a digital watermark is proposed. The performance of the method is evaluated with a digital watermark for a 2D image as an example. In the method, only minimum weight codewords of the code are used as embedded information and two different decoding algorithms are used to reduce the probability of detection error. Analysis and simulation results on the error correcting capability for AWGN channel are shown to ensure the effectiveness of the concept of the method. In the digital watermark, a minimum weight codeword is embedded in the frequency domain of the green plane of the color space of 2D images with a discrete cosine transform as it has a high PSNR with resistance of JPEG compression. Results on an experiment with JPEG compression attack are also shown to ensure the effectiveness of the method.