1-excuse me, last time i was not quiet sure and also what i'm saying now is just my understandings and may not be quiet right. for example i'm not quiet sure about the possiblity of doing the correlation with smaller length correlators.
2-I took a look at my reference and it said :"rapid synchronization of long codes often requiers an estimate of the correlation between recieving code and the despreading one be made in less than a full code period. thus this correlation estimate is based on a partial period...". THIS is the purpose of partial correlation. I dont think that it is a replacement for desired user detection by complete autocorrelation. clearly, partial correlation function is depends upon it's size(the length of correlation window) and it's begining time and it shows the number of agreements (between recieved and despreading code) minus disagreements. think about it....if we use partial correlator as a "desired user code detector" instead of complete correlator, then how can we determine the difference between two DIFFERENT codes that accidentally have the same first 128 bits but differ in remaining bits?! you see, it is not ENOUGH and we need the complete correlator anyhow.
3-As a FPGA designer, may i ask you why do you think "in 1023 length code the FPGA doesnt has enough space to make this corrolation"?!!!!
assuming that you have a 1024 length code. i think it is 1024 bits and it costs you only 1024 flipflops for a shiftregister plus you need some thousands of XORs to do the correlation and it counts NOTHING in any of FPGAs!(I wonder why did you say multiplications! when you are working with bits of data you should use XORs for correlation).
4- My reference is "spread spectrum communiations" by "Ziemer", chapter 3 is about codes and their characteristics. but i think you should search the net for FPGA implementation of spread spectrum reciever...