Linear complexity over Fq and 2-adic complexity of a class of binary generalized cyclotomic sequences with good autocorrelation.

A class of binary sequences with period 2p is constructed using generalized cyclotomic classes, and their linear complexity, minimal polynomial over F q as well as 2-adic complexity are determined using Gauss period and group ring theory. The results show that the linear complexity of these sequences attains the maximum when p ≡ ± 1 (mod 8) and is equal to p+1 when p ≡ ± 3 (mod 8) over extension field. Moreover, the 2-adic complexity of these sequences is maximum. According to Berlekamp–Massey(B–M) algorithm and the rational approximation algorithm (RAA), these sequences have quite good cryptographic properties in the aspect of linear complexity and 2-adic complexity. [ABSTRACT FROM AUTHOR]