According to an Intersil primer on CCK, complementary codes are binary complementary sequences with the mathematical property that their periodic auto-correlative vector sum is zero except at the zero shift. 8-bit complementary code words are used to spread data across a single carrier in 802.11b Direct Sequence Spread Spectrum (DSSS) systems. CCK can send more data using approximately the same bandwidth as the older Barker code because CCK generates complex symbols that carry more bits -- 8 bits at 11 Mbps, 4 bits at 5.5 Mbps.
Radio engineers that want to learn about CCK should read Intersil's excellent primer. Since I'm NOT a radio engineer, I'll stop here!
This was first published in November 2002