Related papers: Some Notes on Constructions of Binary Sequences wi…
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
Spread spectrum multiple access systems demand minimum possible cross-correlation between the sequences within a set of sequences having good auto-correlation properties. Through a connection between generalised Frank sequences and…
The asymptotic behavior of estimates and information criteria in linear models are studied in the context of hierarchically correlated sampling units. The work is motivated by biological data collected on species where autocorrelation is…
We generalize the array orthogonality property for perfect autocorrelation sequences to $n$-dimensional arrays. The generalized array orthogonality property is used to derive a number of $n$-dimensional perfect array constructions.
We examine the correlation of projected rotational velocities in binary systems. It is an extension of previous work (Steinitz and Pyper, 1970; Levato, 1974). An enlarged data basis and new tests enable us to conclude that there is indeed…
1. Basic constructions. 2. Equilibrium and nonequilibrium networks. 3. Equilibrium uncorrelated networks. 4. Nonequilibrium nongrowing scale-free nets. 5. Types of correlations. 6. When pair correlations are important. 7. When loops are…
We introduce a construction for families of 2n-dimensional arrays with asymptotically optimal pairwise cross-correlation. These arrays are constructed using a circulant array of n-dimensional Legendre arrays. We also introduce an…
PAR-constrained sequences are widely used in communication systems and radars due to various practical needs; specifically, sequences are required to be unimodular or of low peak-to-average power ratio (PAR). For unimodular sequence design,…
Correlation between the spins (rotational velocities) in binaries has previously been established. We now continue and show that the degree of spin correlation is independent of the components' separation. Such a result might be related for…
The question of determining a signal from its higher-order autocorrelation data is of practical interest in fields as varied as X-ray crystallography, image processing, and satellite communications. At the heart of the issue is how much of…
We give a method of constructing self-orthogonal codes from equitable partitions of association schemes. By applying this method we construct self-orthogonal codes from some distance-regular graphs. Some of the obtained codes are optimal.…
The majority of star formation results in binaries or higher multiple systems, and planets in such systems are constrained to a limited range of orbital parameters in order to remain stable against perturbations from stellar companions.…
Considering the optimal alignment of two i.i.d. random sequences of length $n$, we show that when the scoring function is chosen randomly, almost surely the empirical distribution of aligned letter pairs in all optimal alignments converges…
The discrepancy of a binary string is the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. In this note we determine the minimal discrepancy that a…
We introduce the notion of minimal inversion sequences for a pattern $\rho$, which form the smallest set of inversion sequences whose avoidance is equivalent to the avoidance of $\rho$ for inversion sequences. We give a characterization of…
Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…
Optical orthogonal codes (OOCs) are sets of $(0,1)$-sequences with good auto- and cross-correlation properties. They were originally introduced for use in multi-access communication, particularly in the setting of optical CDMA…
Circular D0L-systems are those with finite synchronizing delay. We introduce a tool called graph of overhangs which can be used to find the minimal value of synchronizing delay of a given D0L-system. By studying the graphs of overhangs, a…
(a) We propose a ``static'' construction procedure for random networks with given correlations of the degrees of the nearest-neighbor vertices. This is an equilibrium graph, maximally random under the constraint that its degree-degree…
In this paper, we investigate the continuity of linear and sublinear correspondences defined on cones in normed spaces. We also generalize some known results for sublinear correspondences.