Optimal biphase sequences with large linear complexity derived from sequences over Z/sub 4/
P. Udaya, Mohammad Umar Siddiqi · IEEE Transactions on Information Theory · 1996
New families of biphase sequences of size 2/sup r-1/+1, r being a positive integer, are derived from families of interleaved maximal-length sequences over Z/sub 4/ of period 2(2/sup r/-1). These sequences have applications in code-division spread-spectrum multiuser communication systems. The families satisfy the Sidelnikov bound with equality on /spl theta//sub 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 /spl theta//sub max/ with equality. The linear complexity and the period of all sequences are equal to r(r+3)/2 and 2(2/sup r/-1), respectively, with an exception of the single m-sequence which has linear complexity r and period 2/sup r/-1. Sequence imbalance and correlation distributions are also computed.