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.
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.
References
- T. Kasami, “Weight Distribution Formula for Some Class of Cyclic Codes," Tech. Report No. R-285, Univ. of Illinois, 1966.
- L. Welch, “Lower Bounds on the Maximum Cross Correlation of Signals,” IEEE Trans. on Info. Theory, vol. 20, no. 3, pp. 397–399, May 1974.