On Binary Sequences from Recursions “modulo 2e” Made Non-Linear by the Bit-By-Bit “XOR” Function

We consider binary sequences obtained by choosing the the most significant bit of each element in a sequence obtained from a feedback shift register of length n operating over the ring Z/2e, that is with arithmetic carried out modulo 2e. The feedback has been made non-linear by using the bit-by-bit exclusive-or function as well as the linear operation of addition. This should increase the cryptologic strength without greatly increasing the computing overheads. The periods and linear equivalences are discussed. Provided certain conditions are met it is easy to check that the period achieves its maximal value.