Optimal biphase sequences with large linear complexity derived from sequences over Z4

Abstract

New families of biphase sequences of size 2r-1 + 1, r being a positive integer, are derived from families of interleaved maximal-length sequences over Z± of period 2(2r -1). These sequences have applications in code-division spread-spectrum multiuser communication systems. The families satisfy Sidelnikov bound with equality on θmax, which denotes the maximum magnitude of the periodic crosscorreslation and out-of-phase autocorrelation values. One of the families satisfies Welch bound on θmax with equality. The linear complexity and the period of all sequences are equal to r(r + 3)/2 and 2(2r - 1), respectively, with an exception of the single m-sequence which has linear complexity r and perio..