Modified Kasami sequences for CDMA

Kasami sequences yield a set of sequences that have low cross correlation and are applicable in CDMA (code-division multiple-access) communication systems. A Kasami set of sequences is a set of 2^L binary sequences of length N=2^L-1 where L is the degree of the higher order primitive polynomial used to generate the set and is even. The degree of the second primitive polynomial used to generate the Kasami set is L/2. Modified Kasami sequences that are obtained from primitive polynomials of degree L and M are presented. The length of these modified Kasami sequences is the least common multiple of 2^L-1 and 2 ^M-1 (M⩽L), and when M divides L the length of the modified Kasami sequences is 2^L-1. Thus, the modified Kasami sequences reduce to the Kasami sequences when M=L/2