New Sets of Binary and Ternary Sequences with Low Correlation

New binary and ternary sequences with low correlation and simple implementation are presented. The sequences are unfolded from arrays, whose columns are cyclic shifts of a short sequence or constant columns and whose shift sequence (sequence of column shifts) has the distinct difference property. It is known that a binary m-sequence/GMW sequence of length 2 − 1 can be folded row-by-row into an array of 2 − 1 rows of length 2 + 1. We use this to construct new arrays which have at most one column matching for any two dimensional cyclic shift and therefore have low off-peak autocorrelation. The columns of the array can be multiplied by binary orthogonal sequences of commensurate length to produce a set of arrays with low cross-correlation. These arrays are unfolded to produce sequence sets with identical low correlation.