Using the Fourier transform to compute the weight distribution of a binary linear block code

An analytical technique is presented to compute the weight distribution of a linear block code by performing a Fourier analysis involving certain matrices obtained from the code trellis. The proposed method is general, easy to implement, and can be used without having to traverse the trellis or carry out tedious analytical work. The introduced technique can be used as a flexible analytical tool to capture the weight structure of the code with application to problems involving analysis and/or design.