相关论文: Improved Strength Four Covering Arrays with Three …
This paper is motivated by recent developments in group stability, high dimensional expansion, local testability of error correcting codes and topological property testing. In Part I, we formulate and motivate three stability problems: 1.…
The capabilities of multi-antenna technology have recently been significantly enhanced by the proliferation of extra large array architectures. The high dimensionality of these systems implies that communications take place in the nearfield…
We study a new and stronger notion of fault-tolerant graph structures whose size bounds depend on the degree of the failing edge set, rather than the total number of faults. For a subset of faulty edges $F \subseteq G$, the faulty-degree…
It has become standard that, when a SAT solver decides that a CNF $\Gamma$ is unsatisfiable, it produces a certificate of unsatisfiability in the form of a refutation of $\Gamma$ in some proof system. The system typically used is DRAT,…
This paper provides details about experiments in realistic, urban, and frequency flat channels with space-time coding that specifically examines the impact of the number of receive antennas and the design criteria for code selection on the…
Arrayed waveguide gratings (AWGs) are key optical components of various new applications in telecommunication, astrology, medical imaging, and spectroscopy. It is a very powerful integrated light dispersion technology with significant…
We study codes with parameters of $q$-ary shortened Hamming codes, i.e., $(n=(q^m-q)/(q-1), q^{n-m}, 3)_q$. Firstly, we prove the fact mentioned in 1998 by Brouwer et al. that such codes are optimal, generalizing it to a bound for multifold…
In the present note, we study a new method of constructing efficient coverings for Kronecker powers of matrices, recently proposed by J. Alman, Y. Guan, A. Padaki [arXiv, 2022]. We provide an alternative proof for the case of symmetric…
Systems designed with measurement and attestation in mind are often layered, with the lower layers measuring the layers above them. Attestations of such systems, which we call layered attestations, must bundle together the results of a…
Existing graph neural networks typically rely on heuristic choices for hidden dimensions and propagation depths, which often lead to severe information loss during propagation, known as over-squashing. To address this issue, we propose…
Covering numbers are a powerful tool used in the development of approximation algorithms, randomized dimension reduction methods, smoothed complexity analysis, and others. In this paper we prove upper bounds on the covering number of…
The emerging reconfigurable antenna (RA) array technology promises capacity enhancement through dynamic antenna positioning. Traditional approaches enforce half-wavelength or greater spacing among RA elements to avoid mutual coupling,…
A permutation array $A$ is a set of permutations on a finite set $\Omega$, say of size $n$. Given distinct permutations $\pi, \sigma\in \Omega$, we let $hd(\pi, \sigma) = |\{ x\in \Omega: \pi(x) \ne \sigma(x) \}|$, called the Hamming…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
New constraints based on practical hardware are introduced in compressive sensing (CS) based rectangular antenna array thinning technique. In a standard CS array sparsity enforcement, antenna elements are considered as ideal point sources…
Inspired by the "generalized t-designs" defined by Cameron [P. J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835--4842], we define a new class of combinatorial designs which simultaneously provide a generalization…
Linear complementary dual (LCD) codes introduced by Massey are the codes whose intersections with their dual codes are trivial. It can help to improve the security of the information processed by sensitive devices, especially against…
A doubling covering $\U$ of a complex $n$-dimensional manifold $Y$ consists of analytic functions $\psi_j:B_1\to Y$, each function being analytically extendable, as a mapping to $Y$, to a four times larger concentric ball $B_4$. Main result…
This correspondence introduces two new constructive techniques to complete the determination of the sizes of optimal q-ary codes of constant weight three and distance four.
A triple array is a rectangular array containing letters, each letter occurring equally often with no repeats in rows or columns, such that the number of letters common to two rows, two columns, or a row and a column are (possibly…