The structures of partially evaluated Boolean functions are examined, along with the problems that appear when the functions are known on all or most of the inputs of constant weight. Several basic structural theorems are presented. Connections with related areas of mathematics are emphasized. However, the focus is on the algorithmic and computational aspects of the methods. Tests for the order of a function are described and illustrated.>

This paper discusses a number of coding techniques for future satellite communication; they include Reed-Solomon error decoding for message blocks, probabilistic decoding techniques for punctured convolutional codes, and planar Euclidean geometry difference set codes for random multiple access applications. The provision of code concatenation, helical interleaving, and simulation results of new punctured convolutional codes are included. A number of coded satellite systems that demonstrate the usefulness of coding in satellite communications are described.