Polynomial Pseudo-Noise Sequences Based on Algebraic Feedback Shift Registers

To appear in IEEE Transactions on Information Theory.

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science, University of Kentucky, Lexington, KY, 40506-0046, klapper at cs.uky.edu. www.cs.uky.edu/~klapper/andy.html

Mark Goresky, Institute for Advanced Study

Abstract We apply the framework of pi-adic algebra and algebraic feedback shift registers to polynomial rings over finite fields. We give a construction of new pseudorandom sequences over a non-prime finite field that satisfy Golomb's randomness criteria.

Index Terms -- Pseudorandom sequence, Golomb's conjecture, feedback with carry shift register, algebraic feedback shift register, random number generation.