Phased Rapid Sequence Generation Algorithm Implementation And Gold Sequence Search

Pseudo-random sequences with optimal properties such as correlation, high linear spans, balance and long period are widely used in CDMA system, spread spectrum and hopping communication systems. Phase-Controlled (PC) sequence is a new kind of sequence with perfect properties. The PC sequences with period of (2n~1)2 have linear spans no less than n(2~?), five cross-correlation and out-of phase auto-correlation values of { 1,1 ?~, 1 ?n+1 },number of (2敆l) sequences in one family and exact balance for each sequence.Generating GMW sequences is the key to generate PC sequences. By initiating the values of vector description for a primitive element, all finite field elements could be generated by continue cyclic shifting, GMW sequences then could be generated by trace function calculation. And interleaved sequences can be generated after the GMW sequences generated. By rearranging the interleaved sequence with length of (2n~l)2 as an array of (2~?) rows and (2~?) columns and adding GMW sequence with period of (2~?) to each row of the array, a PC sequence could be constructed. Other PC sequences could be constructed by changing the phase of the GMW sequence, this is the name of phase-controlled sequence comes from, and all these PC sequences are not shift equivalent. 66960 PC sequences have been generated by personal computer with CPU of Celeron 400 MHz in less than 12 seconds.The PC sequences are improved in this paper. The linear span of the improved PC sequences is a few times as large as the unimproved by computer simulation verifying and the other properties, such as the balance, the correlation and the number counts in one family, are as same as the unimproved.Also we have searched Gold sequences with different periods of 31,63,127,511,1023,2047,8191 .The number of Gold codes searched is more than that of some other references [12] [22] presented.