Kasami sequences are binarysequences of length2^N−1 whereN is an even integer. Kasami sequences have goodcross-correlation values approaching theWelch lower bound. There are two classes of Kasami sequences—the small set and the large set.

The process of generating a Kasami sequence is initiated by generating amaximum length sequencea(n), wheren = 1…2^N−1. Maximum length sequences are periodic sequences with a period of exactly2^N−1. Next, a secondary sequence is derived from the initial sequence via cyclic decimation sampling asb(n) =a(q ⋅ n), whereq = 2^N/2+1. Modified sequences are then formed by addinga(n) and cyclically time shifted versions ofb(n) using modulo-two arithmetic, which is also termed theexclusive or (xor) operation. Computing modified sequences from all2^N/2 unique time shifts ofb(n) forms the Kasami set of code sequences.

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

• Kasami, Tadao (1966).Weight Distribution Formula for Some Class of Cyclic Codes(PDF) (Technical report). University of Illinois.hdl:2142/74439. R285.
• Welch, Lloyd Richard (May 1974). "Lower Bounds on the Maximum Cross Correlation of Signals".IEEE Transactions on Information Theory.20 (3):397–399.doi:10.1109/TIT.1974.1055219.
• Goiser, Alois M. J. (1998). "4.4 Kasami-Folgen" [Kasami sequences].Handbuch der Spread-Spectrum Technik [Handbook of the spread-spectrum technique] (in German) (1 ed.). Vienna, Austria:Springer Verlag.ISBN 3-211-83080-4.