The weight distribution plays a role to evaluate performance of linear codes and thus was investigated for various codes so far. For a code C of length N, we use AðC; bwNcÞ, called the weight distribution function, to denote the number of code words with normalized weight w. The exponent of the weight distribution gðwÞ 1⁄4 1 N lnAðC; bwNcÞ, called the growth rate, is widely considered instead of the weight distribution itself, since the number of the codewords in C typically increases exponentially with N. Lossy sourced coding for memoryless sources has been widely investigated since Matsunaga and Yamamoto showed that it is possible to attain the rate-distortion bound asymptotically using low-density parity-check (LDPC) codes. Many lossy compression schemes with asymptotic optimal performance have been proposed so far. Efficient lossy compressors with near optimal performance have also been, on the other hand, developed. To treat binary redundant memoryless sources, nonlinear functions were introduced into the decoder, since linear codes cannot provide redundant codewords. It is, therefore, important to study property of a nonlinear code that is a set of the reproduced sequences defined by using nolinear functions. As a first step in investigating a nonlinear code, we evaluate the growth rate of the code using the statistical mechanical approach. It should be, however, noted that the weight distribution is equal to the distance distribution in the case of a linear code, but not equal in the case of a nonlinear code. The analysis addressed here must be, however, expanded to the distance distribution analysis of the nonlinear code. The weight of the codeword z 2 C, which is an N dimensional row vector, is written as WðzÞ 1⁄4 jfi 2 1⁄21; N jxi 1⁄4 1gj. Let AðC; bwNcÞ denote the number of codewords with weight wN in C. Here, w is referred to as the normalized weight. Then, AðC; bwNcÞ can be written as AðC; bwNcÞ :1⁄4 X