Some Applications of the Fourier Transform in Algebraic Coding Theory - Wood, Jay A. (Algebra for Secure and Reliable Communication Modeling, 2015)
This expository article describes two uses of the Fourier transform of interest in algebraic coding theory: the MacWilliams identities on weight enumerators of linear codes and the decomposition of a semi-simple group algebra of a finite group into a direct sum of matrix rings.