Related papers: Binary sequences with a low correlation via cyclot…
In this paper three Schur ring are discussed, namenly: Hamming, circulant orbists and decimated circulant orbits Schur ring. By using autocorrelation function and the run structure of binary sequences we proof the relation between this…
Golay complementary pairs (GCPs) and complete complementary codes (CCCs) have found a wide range of practical applications in coding, signal processing and wireless communication due to their ideal correlation properties. In fact, binary…
There is a well-known bijection between finite binary sequences and integer partitions. Sequences of length r correspond to partitions of perimeter r+1. Motivated by work on rational numbers in the Calkin-Wilf tree, we classify partitions…
This paper is devoted to advancing the theoretical understanding of the iterated immediate snapshot (IIS) complexity of the Weak Symmetry Breaking task (WSB). Our rather unexpected main theorem states that there exist infinitely many values…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
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 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…
Pseudo-geometric designs are combinatorial designs which share the same parameters as a finite geometry design, but which are not isomorphic to that design. As far as we know, many pseudo-geometric designs have been constructed by the…
A special type of cyclic sequences named adjacency-hopping de Bruijn sequences is introduced in this paper. It is theoretically proved the existence of such sequences, and the number of such sequences is derived. These sequences guarantee…
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 recent years, complementary sequence sets have found many important applications in multi-carrier code-division multiple-access (MC-CDMA) systems for their good correlation properties. In this paper, we propose a construction, which can…
Recently, much progress has been made to construct minimal linear codes due to their preference in secret sharing schemes and secure two-party computation. In this paper, we put forward a new method to construct minimal linear codes by…
A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region, called zero correlation zone (ZCZ). Optimal odd-length binary ZCPs (OB-ZCPs) display…
We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on…
The distribution of a given sequence in the set of all sequences with n ones and m = M - n zeros are found by relating the problem to the partitions of a natural number in m natural summands, taking into account the order. The formulas…
Polar codes were introduced by Arikan in 2008 and are the first family of error-correcting codes achieving the symmetric capacity of an arbitrary binary-input discrete memoryless channel under low complexity encoding and using an efficient…
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…
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…
The discrete logarithm is a problem that surfaces frequently in the field of cryptography as a result of using the transformation g^a mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the…
In this paper, the linear complexity over $\mathbf{GF}(r)$ of generalized cyclotomic quaternary sequences with period $2pq$ is determined, where $ r $ is an odd prime such that $r \ge 5$ and $r\notin \lbrace p,q\rbrace$. The minimal value…