Abstract: This paper generalizes three constructions of families of sequences with bounded off peak correlation with application to Code Division Multiple Access (CDMA), frequency hopping, and Ultra Wide Band (UWB). These new families present flexible family sizes and sequence lengths, making them well suited to wireless communications and Multiple Input Multiple Output (MIMO) radar. In particular, we show that the generalized Kamaletdinov I construction offers the lowest off-peak correlation for a given family size. For the two smallest family sizes, this construction asymptotically matches the performance of the small Kasami set and Gold codes, respectively. Among other properties, it has one of the slowest off-peak correlation growth of all known constructions, increasing proportionally to the logarithm of the family size and generates frequency and time hopping sequences.

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