Abstract
General aperiodic correlation bounds named generalised Sarwate bounds are derived, for sequence sets over complex roots of unity with zero or low correlation zone (ZCZ/LCZ), with respect to family size, sequence length, maximum autocorrelation sidelobe, maximum cross-correlation value and the zero or low correlation zone. It is shown that the existing aperiodic binary sequence bounds, such as Sarwate bounds, Welch bounds, Levenshtein bounds, Tang–Fan bounds and Peng–Fan bounds, are only special cases of the presented generalised Sarwate bounds. In addition, the new bounds are also, in general, stronger than the existing aperiodic binary sequence bounds, as well as Boztas aperiodic correlation bounds for normal complex roots-of-unity sequences.
Published Version
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