Kasami code

Not to be confused with Konami Code.

Kasami sequences are binary sequences of length 2^N-1 where N is an even integer. Kasami sequences have good cross-correlation values approaching the Welch lower bound. There are two classes of Kasami sequences - the small set and the large set.

The small set

The process of generating a Kasami sequence is initiated by generating a maximum length sequence a(n), where n=1..2^N-1. Maximum length sequences are periodic sequences with a period of exactly 2^N-1. Next, a secondary sequence is derived from the initial sequence via cyclic decimation sampling as b(n) = a(q*n), where q = 2^N/2+1. Modified sequences are then formed by adding a(n) and cyclically time shifted versions of b(n) using modulo-two arithmetic, which is also termed the exclusive or (xor) operation. Computing modified sequences from all 2^N/2 unique time shifts of b(n) forms the Kasami set of code sequences.

References

• Kasami, T. (1966). Weight Distribution Formula for Some Class of Cyclic Codes (Technical report). University of Illinois. R285.
• Welch, L. (May 1974). "Lower Bounds on the Maximum Cross Correlation of Signals". IEEE Transactions on Information Theory. 20 (3): 397–9. doi:10.1109/TIT.1974.1055219.