Golay kernel 10 decomposition

The efficient Golay correlator for complementary sequences of length 2N has been known since 1991. Its computational efficiency gain compared to direct correlator implementation is comparable to the gain of FFT over DFT implementation. It was used in many applications, the most significant being the RACH preamble in the 3G wireless standard. Presented is a similar correlator for Golay complementary kernels of length 10. This correlator has four stages (building blocks) very similar to the stages of the correlator for Golay sequences of length 2N. It is shown how kernel 10 building blocks can be combined with kernel 2 building blocks to build an efficient correlator of length 2N × 10M. This allows the use of Golay sequences in applications that require a wider range of possible lengths and there is a wider range of autocorrelation functions to choose from. The theoretical importance of this result is that it shows that the kernel sequences (10, 20 and 26) have an internal structure which can lead to further theoretical results.