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

New families of biphase sequences of size 2^r-1+1, r being a positive integer, are derived from families of interleaved maximal-length sequences over Z₄ of period 2(2^r-1). These sequences have applications in code-division spread-spectrum multiuser communication systems. The families satisfy the Sidelnikov bound with equality on θ_max, which denotes the maximum magnitude of the periodic cross-correlation and out-of-phase autocorrelation values. One of the families satisfies the Welch bound on θ_max with equality. The linear complexity and the period of all sequences are equal to r(r+3)/2 and 2(2 ^r-1), respectively, with an exception of the single m-sequence which has linear complexity r and period 2^r-1. Sequence imbalance and correlation distributions are also computed