Pinhui Ke

Xuanyu Liu, Pinhui Ke, Zuling Chang

Sequences exhibiting favorable ambiguity function characteristics play a critical role in radar detection systems and modern mobile communication applications. As a newly developed sequence family, Doppler resilient complementary sequence sets (DRCSSs) can effectively suppress ambiguity function sidelobes by coherently combining the ambiguity functions of their constituent subsequences. The objective of this paper is to present five classes of asymptotically optimal aperiodic DRCSSs with novel parameters based on trace functions over finite fields and column orthogonal complex matrices. Compared with existing asymptotically optimal aperiodic DRCSSs in the literature, the proposed aperiodic DRCSSs deliver superior or novel parameters. Notably, for three families of the constructed aperiodic DRCSSs, the column sequence peak-to-average power ratio (PAPR) is upper bounded by p by selecting suitable column orthogonal complex matrices.

Zhixiong Chen, Vladimir Edemskiy, Pinhui Ke et al.

We investigate the $k$-error linear complexity of pseudorandom binary sequences of period $p^{\mathfrak{r}}$ derived from the Euler quotients modulo $p^{\mathfrak{r}-1}$, a power of an odd prime $p$ for $\mathfrak{r}\geq 2$. When $\mathfrak{r}=2$, this is just the case of polynomial quotients (including Fermat quotients) modulo $p$, which has been studied in an earlier work of Chen, Niu and Wu. In this work, we establish a recursive relation on the $k$-error linear complexity of the sequences for the case of $\mathfrak{r}\geq 3$. We also state the exact values of the $k$-error linear complexity for the case of $\mathfrak{r}=3$. From the results, we can find that the $k$-error linear complexity of the sequences (of period $p^{\mathfrak{r}}$) does not decrease dramatically for $k<p^{\mathfrak{r}-2}(p-1)^2/2$.

Zhifan Ye, Pinhui Ke, Chenhuang Wu

Recently, a conjecture on the linear complexity of a new class of generalized cyclotomic binary sequences of period $p^r$ was proposed by Z. Xiao et al. (Des. Codes Cryptogr., DOI 10.1007/s10623-017-0408-7). Later, for the case $f$ being the form $2^r$ with $r\ge 1$, Vladimir Edemskiy proved the conjecture (arXiv:1712.03947). In this paper, under the assumption of $2^{p-1} \not\equiv 1 \bmod p^2$ and $\gcd(\frac{p-1}{\rm {ord}_{p}(2)},f)=1$, the conjecture proposed by Z. Xiao et al. is proved for a general $f$ by using the Euler quotient. Actually, a generic construction of $p^r$-periodic binary sequence based on the generalized cyclotomy is introduced in this paper, which admits a flexible support set and includes Xiao's construction as a special case, and then an efficient method to compute the linear complexity of the sequence by the generic construction is presented, based on which the conjecture proposed by Z. Xiao et al. could be easily proved under the aforementioned assumption.

Chenhuang Wu, Chunxiang Xu, Zhixiong Chen et al.

We consider the $k$-error linear complexity of a new binary sequence of period $p^2$, proposed in the recent paper "New generalized cyclotomic binary sequences of period $p^2$", by Z. Xiao et al., who calculated the linear complexity of the sequences (Designs, Codes and Cryptography, 2017, https://doi.org/10.1007/s10623-017-0408-7). More exactly, we determine the values of $k$-error linear complexity over $\mathbb{F}_2$ for almost $k>0$ in terms of the theory of Fermat quotients. Results indicate that such sequences have good stability.