Kasami sequences are binary sequences

Séquences

Séquences is a French-language film magazine originally published in Montreal, Quebec by the Commission des ciné-clubs du Centre catholique du cinéma de Montréal, a Roman Catholic film society. Founded in 1955, the publication was edited for forty years by Léo Bonneville, a member of the Clerics...

 of length 2^N-1 where N is an even integer. Kasami sequences have good cross-correlation

Cross-correlation

In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long-duration signal for a shorter, known feature...

 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 starts by generating a maximum length sequence

Maximum length sequence

A maximum length sequence is a type of pseudorandom binary sequence.They are bit sequences generated using maximal linear feedback shift registers and are so called because they are periodic and reproduce every binary sequence that can be reproduced by the shift registers...

a(n), where n=1..2^N-1. Maximum length sequences are periodic sequences so a(n) is repeated periodically for n larger than 2^N-1. Next we generate another sequence b(n) = a(q*n) where q = 2^N/2+1. Kasami sequences are formed by adding a(n) and a time shifted version of b(n) modulo two. The set which is formed by taking all Kasami sequences generated by different time shifts of b(n) plus the a(n) and b(n) sequence forms the Kasami set of sequences. This set has 2^N/2 different sequences.