Related papers: Binary sequences with a low correlation via cyclot…
Binary sequences with minimal autocorrelations have applications in communication engineering, mathematics and computer science. In statistical physics they appear as groundstates of the Bernasconi model. Finding these sequences is a…
Binary periodic sequences with good autocorrelation property have many applications in many aspects of communication. In past decades many series of such binary sequences have been constructed. In the application of cryptography, such…
Binary self-dual codes with large minimum distances, such as the extended Hamming code and the Golay code, are fascinating objects in the coding theory. They are closely related to sporadic simple groups, lattices and invariant theory. A…
Cyclic codes have wide applications in data storage systems and communication systems. Employing two-prime Whiteman generalized cyclotomic sequences of order 6, we construct several classes of cyclic codes over the finite field GF}(q) and…
An orientable sequence of order $n$ over an alphabet $\{0,1,\ldots, k{-}1\}$ is a cyclic sequence such that each length-$n$ substring appears at most once \emph{in either direction}. When $k= 2$, efficient algorithms are known to construct…
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…
For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…
Let $1<g_1<\ldots<g_{\varphi(p-1)}<p-1$ be the ordered primitive roots modulo~$p$. We study the pseudorandomness of the binary sequence $(s_n)$ defined by $s_n\equiv g_{n+1}+g_{n+2}\bmod 2$, $n=0,1,\ldots$. In particular, we study the…
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.
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…
The autocorrelation and the linear complexity of a key stream sequence in a stream cipher are important cryptographic properties. Many sequences with these good properties have interleaved structure, three classes of binary sequences of…
The linear complexity of a periodic sequence over $GF(p^m)$ plays an important role in cryptography and communication [12]. In this correspondence, we prove a result which reduces the computation of the linear complexity and minimal…
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…
Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…
Sequences with high linear complexity have wide applications in cryptography. In this paper, a new class of quaternary sequences over $\mathbb{F}_4$ with period $2p^mq^n$ is constructed using generalized cyclotomic classes. Results show…
Construction of signal sets with low correlation property is of interest to designers of CDMA systems. One of the preferred ways of constructing such sets is the interleaved construction which uses two sequences a and b with 2-level…
Association schemes play an important role in algebraic combinatorics and have important applications in coding theory, graph theory and design theory. The methods to construct association schemes by using bent functions have been…
Certain applications require the use of signals that combine both the capability to operate with low signal-to-noise ratios and the ability to support multiple users without interference. In the case where many users have very different…
Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let $p\ge 5$ be an odd prime and $m$ be…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…