Linear complexity over ${\mathbb{F}_{q}}$ and 2adic complexity of a class of binary generalized cyclotomic sequences with lowvalue autocorrelation
Abstract
A class of binary sequences with period $2p$ is constructed using generalized cyclotomic classes, and their linear complexity, minimal polynomial over ${\mathbb{F}_{q}}$ as well as 2adic complexity are determined using Gauss period and group ring theory. The results show that the linear complexity of these sequences attains the maximum when $p\equiv \pm 1(\bmod~8)$ and is equal to {$p$+1} when $p\equiv \pm 3(\bmod~8)$ over extension field. Moreover, the 2adic complexity of these sequences is maximum. According to BerlekampMassey(BM) algorithm and the rational approximation algorithm(RAA), these sequences have quite good cryptographyic properties in the aspect of linear complexity and 2adic complexity.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 DOI:
 10.48550/arXiv.2109.02095
 arXiv:
 arXiv:2109.02095
 Bibcode:
 2021arXiv210902095W
 Keywords:

 Computer Science  Information Theory
 EPrint:
 23 pages