Theory and applications of q-ary interleaved sequences

A new class of q-ary sequences, called interleaved sequence, is introduced. Their periods, shift equivalence, linear spans, and autocorrelation functions are derived. The interleaved sequences include a large number of popular sequences, such as multiplexed sequences, clock-controlled sequences, Kasami (1966) sequences, GMW sequences, geometric sequences, and No (1989) sequences. A special class of the interleaved sequences is constructed by mapping GF(q^m) sequences into GF(q) sequences in terms of different bases of GF(q^m ) over GF(q). As an application of the theory of interleaved sequences, some new families of binary pseudo-random sequences are constructed, which have large linear spans, optimal periodic cross/autocorrelation functions, balance, and the rapidly “hopped” properties. A complete comparison of the new family of sequences with the Gold sequence family, the Kasami (small and large set) sequence families, the Bent-function sequence family, and the No sequence family is discussed. This shows that the new sequence families have important advantages for use in spread-spectrum multiple-access communication systems