Related papers: Binary sequences with three-valued cross correlati…
3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. The paper concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such…
This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixtures that we propose of Pearson's and…
A sequence of non-negative integers is called a B_k sequence if all the sums of arbitrary k elements are different. In this paper, we will present a new upper bound for B_3 sequences.
An extension to a recently introduced binary neural network is proposed in order to allow the learning of sparse messages, in large numbers and with high memory efficiency. This new network is justified both in biological and informational…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
We report our investigation of 1SWASP J234401.81-212229.1, a variable with a 18461.6 s period. After identification in a 2011 search of the SuperWASP archive for main-sequence eclipsing binary candidates near the distribution's short-period…
We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length 3\ell with the algebraic approach of [9]. In particular, we improve the previous results by…
Recent work (Corradi et al. 2015, Jones et al. 2016) has shown that the phenomenon of extreme abundance discrepancies, where recombination line abundances exceed collisionally excited line abundances by factors of 10 or more, seem to be…
We present results from a high-angular-resolution survey of 78 very low mass (VLM) binary systems with 6.0 <= V-K colour <= 7.5 and proper motion >= 0.15 arcsec/yr. 21 VLM binaries were detected, 13 of them new discoveries. The new binary…
In the present review we summarize direct and indirect evidence that the massive close binary frequency is very large. We then discuss the binary evolutionary processes and we present a general massive close binary evolutionary scheme.…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
Binary cyclic codes have been a hot topic for many years, and significant progress has been made in the study of this types of codes. As is well known, it is hard to construct infinite families of binary cyclic codes [n, n+1/2] with good…
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…
We show that there is a very simple approach to determine the 2-adic complexity of periodic binary sequences with ideal two-level autocorrelation. This is the first main result by H. Xiong, L. Qu, and C. Li, IEEE Transactions on Information…
A binary triangle of size $n$ is a triangle of zeroes and ones, with $n$ rows, built with the same local rule as the standard Pascal triangle modulo $2$. A binary triangle is said to be balanced if the absolute difference between the…
Many data-science applications involve detecting a shared signal between two high-dimensional variables. Using random matrix theory methods, we determine when such signal can be detected and reconstructed from sample correlations, despite…
We review the results of global analyses of short-baseline neutrino oscillation data in 3+1, 3+2 and 3+1+1 neutrino mixing schemes.
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…
Statistics of orbital parameters of binary stars as well as statistics of their physical characteristics bear traces of star formation history. However, statistical investigations of binaries are complicated by lacking or incomplete…
We leverage proof techniques Fourier analysis and an existing result in coding theory to derive new bounds for the problem of non-interactive simulation of binary random variables. Previous bounds in the literature were derived by applying…