Construction of error correcting codes by interpolation

A generalized and unified method of interpolation and transformation is used to generate all known maximal distance codes and important subfield subcodes. Some powerful tools for the analysis and synthesis of maximal distance codes are presented, as well as a generalization of the Mattson-Solomon polynomial and Lagrange and Fourier transforms to more general functions. In certain cases new codes can be obtained by differentiating a kernel function. Some further generalizations of Srivastava codes are constructed. A general method of decoding is given which can be used for complete decoding of ali coset leaders.