CPCH message parts only long scrambling codes apply. Higher layers assign the 224 long and 224 short uplink scrambling codes. 4.3.5.1 Long Scrambling Sequence The long scrambling sequences Clong,1,n and Clong,2,n result from the position wise modulo 2 sum of 38 400 chip segments and two binary m sequences generated by means of two generator polynomials of degree 25. The 1st m sequences, i.e. X comes from the primi- tive (over GF (2)) polynomial X25 + X3 + 1; while the 2nd m sequences, i.e. y comes from the polynomial X25 + X3 + X2 + X + 1. The resulting sequences constitute a seg- The UMTS Network and Radio Access Technology ment set of gold sequences, where the sequence Clong,2,n is a 16777232 chip shifted version of the sequence Clong,1,n [8]. Figure 4.13 illustrates a configuration of long uplink scrambling sequence generator. For completeness in the following we include an extract of the long scrambling se- quence definition from [8]. Where N23...NO = 24 bit binary representation of the scram- bling sequence number n with no as the least significant bit, X sequence which depends on the chosen scrambling sequence number n is denoted Xn, Xn (i) and y(i) denote the ith symbol of the sequence Xn and y, respectively. Then m sequences Xn and y can be de- fined as: = = = (4.4) y(0) = =y(1)=.=y(23)=y(24)= = 1, , (4.5) where xn(0) and y(0) are the initial conditions. The recursive definition of subsequent symbols include: xn(i+25)=x(i+3)+x(i) mod 2, = 0,...,225 27, (4.6) i+25)=y(i+3)+y(i+2)+y(i+1)+y(i) mod = 2, =0,...,225 - 27 . (4.7) The binary gold sequence Zn can be defined as: in(i)=x(i)+y(i) mod 2, i = 0,1,2,,..,225 2, (4.8) then the real valued gold sequence Zn is defined by: (4.9) Now, the real-valued long scrambling sequences Clong,1,n and Clong,2,n are defined as: (4.10) i)= Z,((i+16777232) mod (225 - 1)), =0,1,2,...,225 (4.11) Finally, we define the complex-valued long scrambling sequence Clong,n' as (4.12) = lower integer. The UTRA Physical Layer Design Clong,1,n Clong,2,n Figure 4.13 Configuration of the u