quences. The scrambling codes are repeated for every 10 ms radio frame. If we assume that X and y are two sequences, then X sequence originates from the primi- tive (over GF(2)) polynomial 1 + X + X18, and y sequence results from using the poly- nomial 1 + X5 + X + X10 + X18. The sequence, which depends on the chosen scram- bling code number n, we denote Zn, in the sequel. In addition, we let x(i), y(i) and Zn(i) denote the ith symbol of the sequence X, y, and Zn, respectively. Then from the specifica- tions in [8]we summarize the m sequences X and y as: Initial conditions: x is constructed with x(0)= 1,x(1)x(2)==x(16)=x(17)=0 = = = = = y(0)=y(1)==y(16)=y(17)=1. = Recursive definition of subsequent symbols: (i+18)=x(i+7)+x(i) = mod 2, i =0,...,218- 20, y(i+18)=y(i+10)+y(i+7)+y(i+5)+y(i) mod 2, i = 0,...,218-20 The nth gold code sequence Zn, n = 0,1,2,,..,2" 2, is then defined as = x((i+n) mod mod 2, i=0,...,218-2. (4.43) These resulting binary sequences get converted to real valued sequences Zn by the fol- lowing transformation: The UTRA Physical Layer Design (4.44) Ultimately, we define the nth complex scrambling code sequence Sdl,n as: din(i)=Z,(i)+jZ,((i+131072) mod (218 -1)), 0,1,...,38399, (4.45) where the pattern from phase 0 up to the phase of 38 399 gets repeated. 4.3.12.3 Synchronization Codes The primary synchronization code (PSC), Cpsc results from a so-called generalized hier- archical Golay sequence. It gets chosen to have good aperiodic autocorrelation proper- ties. We express it as: (4.46) Thus, we generate the PSC by repeating the sequence a modulated by a Golay comple- mentary sequence, and creating a complex-valued sequence with identical real and imaginary components. The PSC Cpsc is defined as Cpse=(1+j)x(a,a,a,-a,-a,a,-a,-a,a,a,a,-a,a,-a,a,a), , where the leftmost chip in the sequence corresponds to the chip transmitted first in time. The 16 secondary synchronization codes (SSCs), are complex-valued with identical real and imaginary components, and are constructed from position wise multiplic