Linear complexity over 𝔽_q and 2-adic complexity of a class of binary generalized cyclotomic sequences with low-value autocorrelation

09/05/2021

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by   Yan Wang, et al.

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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( 8) and is equal to p+1 when p≡± 3( 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 cryptographyic properties in the aspect of linear complexity and 2-adic complexity.