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Periodicity, Correlation, and Distribution Properties of d-FCSR sequences

By Mark Goresky and Andrew Klapper


Statistical properties are studied for certain sequences based on the arithmetic of totally ramied extensions of the rational numbers. A simplied exponential representation is found. The arithmetic cross-correlations are shown in some cases to vanish identically. Bounds on the distribution of subsequences are found. Key Words { Cross-correlations, 2-Adic Numbers, Binary Sequences, Number Field. 1 Introduction Pseudorandom sequences have a wide array of uses in computer science and engineering including appications to spread spectrum communication systems, radar systems, signal synchronization, simulation, and cryptography. The pseudorandom sequences in a good family should (a) be easy to generate (possibly with hardware or software), (b) have good distribution properties which make them appear (statistically) to be \random", (c) have low crosscorrelation values so that each sequence may be separated from the others in the family, and (d) arise from some underlying algebraic structu..

Topics: Key Words { Cross-correlations, 2-Adic Numbers, Binary Sequences, Number Field
Year: 2000
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