Related papers: Disproving some theorems in Sharma and Chauhan et …
We provide an amendment to the first theorem of "Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design" by Manchester & Slotine in the form of an additional technical condition required to show…
We investigate a natural subfamily of twisted linearized Reed--Solomon (TLRS) codes in the sum-rank metric, where the twist is applied only to the constant term. We establish a simple necessary and sufficient condition for these codes to be…
Decoherence has the potential to explain all existing neutrino data including LSND results, without enlarging the neutrino sector. This particular form of CPT violation can preserve the equality of masses and mixing angles between particle…
In this comment we address the preprint of Jha and Hirata (arXiv:1809.10316 [physics.chem-ph]) which claims "Numerical Evidence Falsifying Finite-Temperature Many-Body Perturbation Theory." We agree that finite difference differentiation of…
The purpose of this note is to rectify a typographical error in the statements of Theorems 5.5 and 5.6 of Sharma, Chauhan and Singh[3] and further analyze and discuss the significance of the results derived in Takieldin and Sol\'e [4]. In…
Linear code with complementary dual($LCD$) are those codes which meet their duals trivially. In this paper we will give rather alternative proof of Massey's theorem\cite{Massey2}, which is one of the most important characterization of $LCD$…
Counterfactual examples are widely employed to enhance the performance and robustness of large language models (LLMs) through counterfactual data augmentation (CDA). However, the selection of the judge model used to evaluate label flipping,…
Observation of even a single massive cluster, especially at high redshift, can falsify the standard cosmological framework consisting of a cosmological constant and cold dark matter (LCDM) with Gaussian initial conditions by exposing an…
In this paper, we derive a formula for constructing a generator matrix for the intersection of any pair of linear codes over a finite field. Consequently, we establish a condition under which a linear code has a trivial intersection with…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
Support constrained generator matrix for a linear code has been an active topic in recent years. The necessary and sufficient condition for the existence of MDS codes over small fields with support constrained generator matrices were…
Let $\mathbb{F}_{q}$ denote the finite field of order $q,$ let $m_1,m_2,\cdots,m_{\ell}$ be positive integers satisfying $\gcd(m_i,q)=1$ for $1 \leq i \leq \ell,$ and let $n=m_1+m_2+\cdots+m_{\ell}.$ Let…
Detection of parity (P) and time-reversal (T) symmetry-odd electric dipole moments (EDMs) within currently achievable resolution would evidence physics beyond the Standard Model of particle physics. Via the CPT-theorem, which includes…
Recent calculations of nuclear structure corrections to the Lamb shift in light muonic atoms are based on an expansion in a parameter eta, where only terms up to second order are retained. The parameter eta can be shown to be proportional…
Our result in cond-mat/0305147 that, instead of the conventional heat fluctuation theorem (FT), a new FT holds for heat fluctuations for a Brownian particle in a moving confining potential[Wang et al. 2002], was claimed to be disproved in a…
The main aim of this paper is to study $LCD$ codes. Linear code with complementary dual($LCD$) are those codes which have their intersection with their dual code as $\{0\}$. In this paper we will give rather alternative proof of Massey's…
We characterize the structure of 2-quasi-cyclic codes over a finite field F by the so-called Goursat Lemma. With the characterization, we exhibit a necessary and sufficient condition for a 2-quasi-cyclic code being a dihedral code. And we…
Providing explanations about how machine learning algorithms work and/or make particular predictions is one of the main tools that can be used to improve their trusworthiness, fairness and robustness. Among the most intuitive type of…
The problem of robustly reconstructing an integer vector from its erroneous remainders appears in many applications in the field of multidimensional (MD) signal processing. To address this problem, a robust MD Chinese remainder theorem…
We systematically study the fundamental competition between quantum error correction (QEC) and continuous symmetries, two key notions in quantum information and physics, in a quantitative manner. Three meaningful measures of approximate…