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Sequences are often used as a basis for code division multiplexing. In order that minimum interference from other users should occur, it is important that the sequences used should have good crosscorrelation properties. Various sets of sequences have been derived with appropriate properties, but the sources have been well dispersed within the literature. In the paper are collected six of the most important of these sequence sets, and examples are given of the way in which they are constructed.

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We present a new family of one-coincidence sequence sets suitable for frequency hopping code division multiple access (FH-CDMA) systems with dispersed (low density) sequence elements. These sets are derived from one-coincidence prime sequence sets, such that for each one-coincidence prime sequence set there is a new one-coincidence set comprised of sequences with dispersed sequence elements, required in some circumstances, for FH-CDMA systems. Getting rid of crowdedness of sequence elements is achieved by doubling the size of the sequence element alphabet. In addition, this doubling process eases control over the distance between adjacent sequence elements. Properties of the new sets are discussed.2010 Mathematics Subject Classification. Primary 94A12, 94A15, 94.10; Secondary 11B50.

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