Partial Period Autocorrelations of Geometric Sequences

IEEE Transactions on Information Theory 40 (1994) 494-502.

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science, University of Kentucky, Lexington, KY, 40506-0046, klapper at
Mark Goresky, Institute for Advanced Study

Abstract For a binary pseudorandom sequence $\{\bS_i\}$ with period $N$, the partial period autocorrelation function $A_\bS (\tau, k, D)$ is defined by correlating the portion of the sequence within a window of size $D$, and start position $k$, with the portion in another window of the same size but starting $\tau$ steps later in the sequence. A distribution of possible partial period autocorrelation values is obtained by allowing the start position $k$ to vary over all possible values $0 \le k Index Terms -- Binary Sequence, Aperiodic Autocorrelation, Finite Fields, Spread Spectrum, Synchronization.