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.

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