Gold code

A Gold code is a set of binary sequences, used in telecommunication (CDMA) [" [George, M., Hamid, M., and Miller A. PDFlink| [http://www.xilinx.com/support/documentation/application_notes/xapp217.pdf Gold Code Generators in Virtex Devices] ] and satellite navigation (GPS) [" [http://www.kowoma.de/en/gps/signals.htm GPS - explained (Signals)] "] . Gold Codes are named after [http://www.rgcsystems.com/ppl1_gold.htm Robert Gold] .

Pick two "m"-sequences of the same length "n", such that their cross-correlation takes just three values. The set of the "n" exclusive-ors of the two sequences in their various phases (i.e. translated into all relative positions), together with the two "n"-sequences themselves, is a set of Gold codes.

The exclusive or of two Gold codes is another Gold code in some phase.

A set of gold sequences consist of 2^{"m" + 1 sequences each one with a period of 2"m" − 1.}

All 2^{"m" + 1 sequences are balanced and contain either 2"m"−1 ones and 2"m"−1 − 1 zeros or 2"m"−1 − 1 ones and 2"m"−1 zeros.}

References

*Gold, R. "Optimal binary sequences for spread spectrum multiplexing (Corresp.)", IEEE Transactions on Information Theory, volume 13,number 4,pages 619--621, 1967.

ee also

*Kasami code
*Complementary sequences