Related papers: Binary sequences with a low correlation via cyclot…
Due to wide applications of binary sequences with low correlation to communications, various constructions of such sequences have been proposed in literature. However, most of the known constructions via finite fields make use of the…
In the realm of modern digital communication, cryptography, and signal processing, binary sequences with a low correlation properties play a pivotal role. In the literature, considerable efforts have been dedicated to constructing good…
Motivated by the constructions of binary sequences by utilizing the cyclic elliptic function fields over the finite field $\mathbb{F}_{2^{n}}$ by Jin \textit{et al.} in [IEEE Trans. Inf. Theory 71(8), 2025], we extend the construction to…
Binary cyclic codes are worth studying due to their applications and theoretical importance. It is an important problem to construct an infinite family of cyclic codes with large minimum distance $d$ and dual distance $d^{\perp}$. In recent…
Let $n_1$ and $n_2$ be two distinct primes with $\mathrm{gcd}(n_1-1,n_2-1)=4$. In this paper, we compute the autocorrelation values of generalized cyclotomic sequence of order $4$. Our results show that this sequence can have very good…
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…
Low correlation (finite length) sequences are used in communications and remote sensing. One seeks codebooks of sequences in which each sequence has low aperiodic autocorrelation at all nonzero shifts, and each pair of distinct sequences…
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 cyclic codes having large dimensions and minimum distances close to the square-root bound are highly valuable in applications where high-rate transmission and robust error correction are both essential. They provide an optimal…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…
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…
An orientable sequence of order $n$ is a cyclic binary sequence such that each length-$n$ substring appears at most once \emph{in either direction}. Maximal length orientable sequences are known only for $n\leq 7$, and a trivial upper bound…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
Binary sequences are widely used in various practical fields, such as telecommunications, radar technology, navigation, cryptography, measurement sciences, biology or industry. In this paper, a method to generate long binary sequences (LBS)…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
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…
In this paper, we survey constructions of and nonexistence results on combinatorial/geometric structures which arise from unions of cyclotomic classes of finite fields. In particular, we survey both classical and recent results on…
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…
The construction of self-dual codes over small fields such that their minimum distances are as large as possible is a long-standing challenging problem in the coding theory. In 2009, a family of binary self-dual cyclic codes with lengths…