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Product sequences with good correlation properties

The structure of the autocorrelation function of sequences which are the products of factor sequences with known autocorrelation functions is investigated. A means of constructing binary sequences with good correlation properties is presented. It is also shown that this procedure, when applied to sets of sequences, preserves the cross-correlation properties of the factor sequences. The results are also extended to the non-binary case where it is also demonstrated that sequences with similar segmentation and correlation structures to q-ary m-sequences can be constructed which have lengths other than q n − 1.