Related papers: Comments on "A New Method to Compute the 2-Adic Co…
This paper contributes to compute 2-adic complexity of two classes of Ding-Helleseth generalized cyclotomic sequences. Results show that 2-adic complexity of these sequences is good enough to resist the attack by the rational approximation…
Binary sequences with optimal autocorrelation and large linear complexity have important applications in cryptography and communications. Very recently, a class of binary sequences of period $4p$ with optimal autocorrelation was proposed…
We examine the linear complexity and the autocorrelation properties of new quaternary cyclotomic sequences of period 2p. The sequences are constructed via the cyclotomic classes of order four.
Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there have been significant advancements in the topic of complexity measures for randomness assessment, which are of fundamental importance in theoretical…
Tang and Ding \cite{X. Tang} present a series of quaternary sequences $w(a, b)$ interleaved by two binary sequences $a$ and $b$ with ideal autocorrelation and show that such interleaved quaternary sequences have optimal autocorrelation. In…
We investigate the $k$-error linear complexity over $\mathbb{F}_p$ of binary sequences of length $2p$ with optimal three-level autocorrelation. These balanced sequences are constructed by cyclotomic classes of order four using a method…
Aperiodic autocorrelation is an important indicator of performance of sequences used in communications, remote sensing, and scientific instrumentation. Knowing a sequence's autocorrelation function, which reports the autocorrelation at…
In this paper, we determine the linear complexity of a class of new binary cyclotomic sequences of period pn constructed by Z. Xiao et al. (Des. Codes Cryptogr. DOI 10.1007/s10623-017-0408-7) and prove their conjecture about high linear…
We analyze the connection between the autocorrelation of a binary sequence and its run structure given by the run length encoding. We show that both the periodic and the aperiodic autocorrelation of a binary sequence can be formulated in…
We first introduce a family of binary $pq^2$-periodic sequences based on the Euler quotients modulo $pq$, where $p$ and $q$ are two distinct odd primes and $p$ divides $q-1$. The minimal polynomials and linear complexities are determined…
A general construction of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic and this construction, several classes of binary sequences with optimal autocorrelation and other…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and…
Constructions of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic, several more general constructions of binary sequences with optimal autocorrelations and other low…
Binary sequences with lower autocorrelation values have important applications in cryptography and communications. In this paper, we present all possible parameters for binary periodical sequences with a 2-level autocorrelation values. For…
Binary sequences with good autocorrelation properties and large linear complexity are useful in stream cipher cryptography. The Sidelnikov-Lempel-Cohn-Eastman (SLCE) sequences have nearly optimal autocorrelation. However, the problem of…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
Properties of 2-adic valuation sequences for general quadratic polynomials with integer coefficients are determined directly from the coefficients. These properties include boundedness or unboundedness, periodicity, and valuations at…
We estimate the maximum-order complexity of a binary sequence in terms of its correlation measures. Roughly speaking, we show that any sequence with small correlation measure up to a sufficiently large order $k$ cannot have very small…
Sequences with {\em perfect linear complexity profile} were defined more than thirty years ago in the study of measures of randomness for binary sequences. More recently {\em apwenian sequences}, first with values $\pm 1$, then with values…