Related papers: New Optimal Binary Sequences with Period $4p$ via …
This work studies the application of the discrete Holder-Brascamp-Lieb (HBL) inequalities to the design of communication optimal algorithms. In particular, it describes optimal tiling (blocking) strategies for nested loops that lack data…
Beam search is a go-to strategy for decoding neural sequence models. The algorithm can naturally be viewed as a subset optimization problem, albeit one where the corresponding set function does not reflect interactions between candidates.…
Optical single-short measurement of the cross-correlation function between periodic sequences is demonstrated. The sequences are encoded into the broadband ultrashort phase-shaped pulses which are mixed in the nonlinear medium with…
There exists a large literature of construction of convolutional codes with maximal or near maximal free distance. Much less is known about constructions of convolutional codes having optimal or near optimal column distances. In this paper,…
Temporal correlations in the time series observed in various systems have been characterized by the autocorrelation function. Such correlations can be explained by heavy-tailed interevent time distributions as well as by correlations…
In cryptography, we hope a sequence over $\mathbb{Z}_m$ with period $N$ having larger $m$-adic complexity. Compared with the binary case, the computation of 4-adic complexity of knowing quaternary sequences has not been well developed. In…
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…
Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data storage systems. The objective of this paper is to give eight…
Negative orientable sequences, i.e. periodic sequences with elements from a finite alphabet of size at least three in which an n-tuple or the negative of its reverse appears at most once in a period of the sequence, were introduced by…
Maintaining the pair similarity relationship among originally high-dimensional data into a low-dimensional binary space is a popular strategy to learn binary codes. One simiple and intutive method is to utilize two identical code matrices…
Complex-valued periodic sequences, u, constructed by Goran Bjorck, are analyzed with regard to the behavior of their discrete periodic narrow-band ambiguity functions A_p(u). The Bjorck sequences, which are defined on Z/pZ for p>2 prime,…
Kim et al. (2021) gave a method to embed a given binary $[n,k]$ code $\mathcal{C}$ $(k = 3, 4)$ into a self-orthogonal code of the shortest length which has the same dimension $k$ and minimum distance $d' \ge d(\mathcal{C})$. We extend this…
Intersection graphs are well-studied in the area of graph algorithms. Some intersection graph classes are known to have algorithms enumerating all unlabeled graphs by reverse search. Since these algorithms output graphs one by one and the…
The classical Fibonacci sequence is known to exhibit many fascinating properties. In this paper, we explore the Fibonacci sequence and integer sequences generated by second order linear recurrence relations with positive integer…
In this paper, code decompositions (a.k.a. code nestings) are used to design binary polarization kernels. The proposed kernels are in general non-linear. They provide a better polarization exponent than the previously known kernels of the…
There is a one-to-one correspondence between $\ell$-quasi-cyclic codes over a finite field $\mathbb F_q$ and linear codes over a ring $R = \mathbb F_q[Y]/(Y^m-1)$. Using this correspondence, we prove that every $\ell$-quasi-cyclic self-dual…
We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…
We present a framework for designing differentially private (DP) mechanisms for binary functions via a graph representation of datasets. Datasets are nodes in the graph and any two neighboring datasets are connected by an edge. The true…
We develop a technique for estimating the inner eccentricity in hierarchical triple systems with well separated components. We investigate systems with initially circular and coplanar orbits and comparable masses. The technique is based on…
We construct a seven-term exact sequence involving low degree cohomology spaces of a Lie algebra $\Lg$, an ideal $\Lh$ of $\Lg$ and the quotient $\Lg / \Lh$ with coefficients in a $\Lg$-module. The existence of such a sequence follows from…