Kasami code

Not to be confused with Konami Code.

Kasami sequences, named after Japanese information theorist Tadao Kasami, 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. They are used as low-correlation spreading sequences in spread-spectrum communication systems. There are two classes of Kasami sequences—the small set and the large set.

Kasami 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.

See also

• Gold sequence (aka Gold code)
• JPL sequence (aka JPL code)

References

• Kasami, Tadao (1966). Weight Distribution Formula for Some Class of Cyclic Codes (PDF) (Technical report). University of Illinois. hdl:2142/74439. R285.
• Welch, Lloyd Richard (May 1974). "Lower Bounds on the Maximum Cross Correlation of Signals". IEEE Transactions on Information Theory. 20 (3): 397–399. doi:10.1109/TIT.1974.1055219.
• Goiser, Alois M. J. (1998). "4.4 Kasami-Folgen" [Kasami sequences]. Handbuch der Spread-Spectrum Technik [Handbook of the spread-spectrum technique] (in German) (1 ed.). Vienna, Austria: Springer Verlag. ISBN 3-211-83080-4.