Kasami code

Kasami sequences are binary sequences of length 2N-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.

Not to be confused with Konami Code.

The small set

The process of generating a Kasami sequence is initiated by generating a maximum length sequence a(n), where n=1..2N-1. Maximum length sequences are periodic sequences with a period of exactly 2N-1. Next, a secondary sequence is derived from the initial sequence via cyclic decimation sampling as b(n) = a(q*n), where q = 2N/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 2N/2 unique time shifts of b(n) forms the Kasami set of code sequences.

gollark: ++eval 1 + 1
gollark: ++help
gollark: Because.
gollark: This is for testing my discord bot now.
gollark: ++eval 1 >> 3

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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