Kasami 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.

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.