Related papers: Good cyclic codes and the uncertainty principle
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms which enable to deduce global information about some data by…
As a subclass of linear codes, cyclic codes have efficient encoding and decoding algorithms, so they are widely used in many areas such as consumer electronics, data storage systems and communication systems. In this paper, we give a…
We discuss control techniques for noisy self-sustained oscillators with a focus on reliability, stability of the response to noisy driving, and oscillation coherence understood in the sense of constancy of oscillation frequency. For any…
A Hamiltonian formalism is used to describe ensembles of fields in terms of two canonically conjugate functionals (one being the field probability density). The postulate that a classical ensemble is subject to nonclassical fluctuations of…
Motivated from Deutsch entropic uncertainty principle and several product uncertainty principles, we derive an uncertainty principle for the product of entropies using functions.
Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such…
The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the…
Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…
A matching from a finite subset $A\subset\mathbb{Z}^n$ to another subset $B\subset\mathbb{Z}^n$ is a bijection $f : A \rightarrow B$ with the property that $a+f(a)$ never lies in $A$. A matching is called acyclic if it is uniquely…
Uncertainty principle forbids one to determine which of the two paths a quantum system has travelled, unless interference between the alternatives had been destroyed by a measuring device, e.g., by a pointer. One can try to weaken the…
We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…
The classical support uncertainty principle states that the signal and its discrete Fourier transform (DFT) cannot be localized simultaneously in an arbitrary small area in the time and the frequency domain. The product of the number of…
Software testing is a mandatory activity in any serious software development process, as bugs are a reality in software development. This raises the question of quality: good tests are effective in finding bugs, but until a test case…
A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with…
Here we present a Bayesian formalism for the goodness-of-fit that is the evidence for a fixed functional form over the evidence for all functions that are a general perturbation about this form. This is done under the assumption that the…
One of the classical problems in group theory is determining the set of positive integers $n$ such that every group of order $n$ has a particular property $P$, such as cyclic or abelian. We first present the Sylow theorems and the idea of…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a class of three-weight…
Cyclic codes have been widely used in digital communication systems and consume electronics as they have efficient encoding and decoding algorithms. The weight distribution of cyclic codes has been an important topic of study for many…
Code language models are increasingly adopted for both understanding and generative tasks. Despite their success, these models frequently produce overconfident incorrect predictions and underconfident correct predictions, undermining their…