Linear complexity over ${\mathbb{F}_{q}}$ and 2-adic complexity of a class of binary generalized cyclotomic sequences with low-value 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 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 $p\equiv \pm 1(\bmod~8)$ and is equal to {$p$+1} when $p\equiv \pm 3(\bmod~8)$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2021
- DOI:
- 10.48550/arXiv.2109.02095
- arXiv:
- arXiv:2109.02095
- Bibcode:
- 2021arXiv210902095W
- Keywords:
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- Computer Science - Information Theory
- E-Print:
- 23 pages