## Linear complexity and trace representation of quaternary sequences over ℤ 4 $\mathbb {Z}_{4}$ based on generalized cyclotomic classes modulo pq

- Zhixiong Chen
- Cryptography and Communications
- 2016

1 Excerpt

- Published 2008 in IEEE Transactions on Information Theory

Family A is a family of sequences of period 2<sup>n</sup> - 1 over Zi, the ring of integers modulo 4. This family has optimal correlation properties and its correlation distribution is well known. Two related families of quaternary sequences are the families B and C. These are families of sequences over Z<sub>4</sub> of period 2(2<sup>n</sup> - 1). In recent years, new families of quaternary sequences of period 2(2<sup>n</sup> - 1) have been constructed by modifying the sequence families B and C in a nonlinear way. This has resulted in a new family D of sequences of period 2(2<sup>n</sup> - 1) which has optimal correlation properties, but until now the correlation distribution of this family has not been known. In this paper, we completely determine the correlation distribution of family D by making use of properties of exponential sums.

@article{Johansen2008TheCD,
title={The Correlation Distribution of Quaternary Sequences of Period \$2(2^n-1)\$ },
author={Aina Johansen and Tor Helleseth and Xiaohu Tang},
journal={IEEE Transactions on Information Theory},
year={2008},
volume={54},
pages={3130-3139}
}