An approach to finding codes for use in direct sequencespread spectrum communications systems is described. Itis based upon an analogy between codes having auto- andcross-correlation properties desirable for spreadspectrum systems, and certain dynamical systemsencountered in ergodic theory called systems with Lebesgue spectrum. Such systems are associated withcollections of orthogonal functions and these functionscan be used to generate collections of time series withzero cross-correlation functions. To generate codewordswe must use truncated versions of these time series,for which the cross-correlations are no longerprecisely zero: these truncated sequences correspond toperiodic orbits of the dynamical system. The method forfinding a code from a suitable periodic orbit isdescribed, and an example, using a simple dynamicalsystem known as the doubling map, is worked through insome detail.
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