// Workers AI · dad joke modeWhy did Kasami code go to therapy? It had too many errors to correct.

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.