Related papers: Low Autocorrelation Binary Sequences: Number Theor…
We present a method for detection of weak continuous signals from sources in binary systems via the incoherent combination of many "short" coherently-analyzed segments. The main focus of the work is on the construction of a metric on the…
It is proved in this work that exhaustively determining bad patterns in arbitrary, finite low-density parity-check (LDPC) codes, including stopping sets for binary erasure channels (BECs) and trapping sets (also known as near-codewords) for…
We describe the discovery of a 0.68+0.52 solar mass eclipsing binary (EB) with an 8.4-day orbital period, found through a systematic search of ten fields of the Trans-atlantic Exoplanet Survey (TrES). Such long-period low-mass EBs…
The paper introduces new bounds on the asymptotic density of parity-check matrices and the achievable rates under ML decoding of binary linear block codes transmitted over memoryless binary-input output-symmetric channels. The lower bounds…
We consider the lossless compression bound of any individual data sequence. If we fit the data by a parametric model, the entropy quantity $nH({\hat \theta}_n)$ obtained by plugging in the maximum likelihood estimate is an underestimate of…
In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices. The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes…
In the literature, compact binary coalescences (CBCs) have been proposed as one of the main scenarios to explain the origin of some non-repeating fast radio bursts (FRBs). The large discrepancy between the FRB and CBC event rate densities…
The period distribution of contact binaries exhibits a very sharp short period cut-off at 0.22 days. In order to provide valuable information on this short period limit, we observed ten totally eclipsing contact binaries with orbital…
Results of an exhaustive search for minimum peak sidelobe level binary sequences are presented. Several techniques for efficiency implementation of search algorithm are described. A table of number of non-equivalent optimal binary sequences…
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check codes and variations…
A lower bound on the number of uncorrectable errors of weight half the minimum distance is derived for binary linear codes satisfying some condition. The condition is satisfied by some primitive BCH codes, extended primitive BCH codes,…
We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in $\text{Quasi-NP} = \text{NTIME}[n^{(\log n)^{O(1)}}]$ and…
The approximate degree of a Boolean function is the minimum degree of real polynomial that approximates it pointwise. For any Boolean function, its approximate degree serves as a lower bound on its quantum query complexity, and generically…
Perturbative QCD with nf flavours of massless quarks becomes simple in the hypothetical limit nf -> 16.5, where the leading beta-function coefficient vanishes. The Banks-Zaks (BZ) expansion in a0=(8/321)(16.5-nf) is straightforward to…
We study variable-length feedback (VLF) codes over binary-input memoryless symmetric (BMS) channels using posterior matching with small-enough-difference (SED) partitioning. Prior analyses of SED-based schemes rely on bounded log-likelihood…
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…
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)…
Recall that a binary linear code of length $n$ is a linear subspace $\mathcal{C} = \{x\in\mathbb{F}_2^n\mid Ax=0\}$. Here the parity check matrix $A$ is a binary $m\times n$ matrix of rank $m$. We say that $\mathcal{C}$ has rate $R=1-\frac…
In this correspondence, for every periodic $p-$ary sequence satisfying ideal two-level autocorrelation property the existence of an element of the field ${\bf GF}(p)$ which appears one time less than all the rest that are equally…
Blazars' non-thermal emission shows rapid variability across all wavelengths, so spectral energy distributions (SEDs) built from quasi-simultaneous data are crucial for revealing the jets physical properties. In this work, we construct…