Related papers: A General Construction of Binary Sequences with Op…
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…
There exists a large literature of construction of convolutional codes with maximal or near maximal free distance. Much less is known about constructions of convolutional codes having optimal or near optimal column distances. In this paper,…
The generalized binary sequences of order 2 have been used to construct good binary cyclic codes [4]. The linear complexity of these sequences has been computed in [2]. The autocorrelation values of such sequences have been determined in…
We formulate learning of a binary autoencoder as a biconvex optimization problem which learns from the pairwise correlations between encoded and decoded bits. Among all possible algorithms that use this information, ours finds the…
We define a new class of binary matrices by maximizing the peak-sidelobe distances in the aperiodic autocorrelations. These matrices can be used as robust position marks for in-plane spatial alignment. The optimal square matrices of…
The autocorrelation of a sequence is a useful criterion, among all, of resistance to cryptographic attacks. The behavior of the autocorrelations of random Boolean functions (studied by Florian Caullery, Eric F\'erard and Fran\c{c}ois Rodier…
Sequences with good randomness properties are quite important for stream ciphers. In this paper, a new class of quaternary sequences is constructed by using generalized cyclotomic classes of $\mathbb{Z}_{2p^m}$ $(m\geq1)$. The exact values…
Sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. Among the known sequences, cyclotomic families have the optimal autocorrelation property. In this paper, we…
Binary sequences with low autocorrelations are important in communication engineering and in statistical mechanics as groundstates of the Bernasconi-model. Computer searches are the main tool to construct such sequences. Due to the…
An $m$-sequence is the one of the largest period among those produced by a linear feedback shift register. It possesses several desirable features of pseudorandomness such as balance, uniform pattern distribution and ideal autocorrelation…
In this paper, a new method is presented to compute the 2-adic complexity of pseudo-random sequences. With this method, the 2-adic complexities of all the known sequences with ideal 2-level autocorrelation are uniformly determined. Results…
This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences…
Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared to random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation…
Via interleaving Ding-Helleseth-Lam sequences, a class of binary sequences of period $4p$ with optimal autocorrelation magnitude was constructed in \cite{W. Su}. Later, Fan showed that the linear complexity of this class of sequences is…
Analogously to de Bruijn sequences, orientable sequences have application in automatic position-location applications and, until recently, studies of these sequences focused on the binary case. In recent work by Alhakim et al., a range of…
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…
This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any n-tuple occurs at most once in a period in either direction. As has been previously described, such…
The search for binary sequences with a high figure of merit, known as the low autocorrelation binary sequence ($labs$}) problem, represents a formidable computational challenge. To mitigate the computational constraints of the problem, we…
This paper proposes a new class of random sequences called binary primes tableau (PT) sequences that have potential applications in cryptography and communications. The PT sequence of rank p is obtained from numbers arranged in a tableau…
We investigate the behavior of optimal alignment paths for homologous (related) and independent random sequences. An alignment between two finite sequences is optimal if it corresponds to the longest common subsequence (LCS). We prove the…