Kasami code

Not to be confused with Konami 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.

See also

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