Abstract
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\(^{\rm 2{\it m}}\) – 1 can be folded row-by-row into an array of 2m – 1 rows of length 2m + 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.
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© 2005 Springer-Verlag Berlin Heidelberg
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Krengel, E.I., Tirkel, A.Z., Hall, T.E. (2005). New Sets of Binary and Ternary Sequences with Low Correlation. In: Helleseth, T., Sarwate, D., Song, HY., Yang, K. (eds) Sequences and Their Applications - SETA 2004. SETA 2004. Lecture Notes in Computer Science, vol 3486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11423461_15
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DOI: https://doi.org/10.1007/11423461_15
Publisher Name: Springer, Berlin, Heidelberg
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