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Related papers: Spectral Bounds for Quasi-Twisted Codes

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We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…

General Relativity and Quantum Cosmology · Physics 2024-07-11 Gioel Calabrese , Carsten Gundlach

This article studies one-generator and two-generator quasi-cyclic codes over finite fields. We present two versions of necessary and sufficient conditions for the symplectic selforthogonality of one-generator quasi-cyclic codes, using both…

Information Theory · Computer Science 2024-12-19 Tushar Bag , Hai Q Dinh , Daniel Panario

BCH codes are an interesting class of cyclic codes due to their efficient encoding and decoding algorithms. In the past sixty years, a lot of progress on the study of BCH codes has been made, but little is known about the properties of…

Information Theory · Computer Science 2023-12-12 Xiaoqiang Wang , Chengliang Xiao , Dabin Zheng

Cyclic codes over finite fields are widely employed in communication systems, storage devices and consumer electronics, as they have efficient encoding and decoding algorithms. BCH codes, as a special subclass of cyclic codes, are in most…

Information Theory · Computer Science 2016-11-02 Shuxing Li , Cunsheng Ding , Maosheng Xiong , Gennian Ge

The tensor product of one code endowed with the Hamming metric and one endowed with the rank metric is analyzed. This gives a code which naturally inherits the sum-rank metric. Specializing to the product of a cyclic code and a skew-cyclic…

Information Theory · Computer Science 2021-06-01 Gianira N. Alfarano , F. J. Lobillo , Alessandro Neri , Antonia Wachter-Zeh

We propose an algorithm to find a lower bound for the number of cyclic codes over any finite field with any given exponent. Besides, we give a formula to find the exponent of BCH codes.

Information Theory · Computer Science 2022-09-01 Anuj Kumar Bhagat , Ritumoni Sarma

In this work we start the investigation of tight complexity bounds for connectivity problems parameterized by cutwidth assuming the Strong Exponential-Time Hypothesis (SETH). Van Geffen et al. posed this question for odd cycle transversal…

Data Structures and Algorithms · Computer Science 2022-12-26 Narek Bojikian , Vera Chekan , Falko Hegerfeld , Stefan Kratsch

By using the Cowling approximation, quasi-radial modes of rotating general relativistic stars are computed along equilibrium sequences from non-rotating to maximally rotating models. The eigenfrequencies of these modes are decreasing…

Astrophysics · Physics 2008-11-26 S'i. Yoshida , Y. Eriguchi

We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular,…

Optimization and Control · Mathematics 2023-10-03 Oleg R. Musin

We consider eigenvalues of a quantized cat map (i.e. hyperbolic symplectic integer matrix), cut off in phase space to include a fixed point as its only periodic orbit on the torus. We prove a simple formula for the eigenvalues on both the…

Spectral Theory · Mathematics 2022-05-12 Yonah Borns-Weil

Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to…

Information Theory · Computer Science 2026-05-25 Gustavo Terra Bastos , Angelynn Álvarez , Cameron Williams

In this paper we provide new compact integral expressions and associated simple asymptotic approximations for converse and achievability bounds in the finite blocklength regime. The chosen converse and random coding union bounds were taken…

Information Theory · Computer Science 2016-10-25 Tomaso Erseghe

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on…

Information Theory · Computer Science 2013-07-17 Igal Sason

We consider the coding problem in the Stiefel manifold with chordal distance. After considering various low-dimensional instances of this problem, we use Rankin's bounds on spherical codes to prove upper bounds on the minimum distance of a…

Metric Geometry · Mathematics 2024-07-03 John Jasper , Nathan Mankovich , Dustin G. Mixon

Spectra of suitably chosen Pisot-Vijayaraghavan numbers represent non-trivial examples of self-similar Delone point sets of finite local complexity, indispensable in quasicrystal modeling. For the case of quadratic Pisot units we…

Number Theory · Mathematics 2020-10-09 Petr Ambrož , Zuzana Masáková , Edita Pelantová

The squashed entanglement is a widely used entanglement measure that has many desirable properties. However, as it is based on an optimization over extensions of arbitrary dimension, one drawback of this measure is the lack of good…

Quantum Physics · Physics 2022-03-08 Hamza Fawzi , Omar Fawzi

Quasi-bound states in the continuum (q-BICs) are resonant states of suitably tailored nanostructures with long optical lifetimes controlled by symmetry-breaking perturbations. While in planarized ultrathin devices the resulting Fano…

Optics · Physics 2021-02-24 Adam Overvig , Nanfang Yu , Andrea Alu

For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.

Probability · Mathematics 2022-12-27 Tomohiro Nishiyama

We provide bounds for codes for a non-symmetric channel or, equivalently, for ternary codes with the Manhattan distance.

Information Theory · Computer Science 2010-04-12 Ludo Tolhuizen

This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant…

Information Theory · Computer Science 2021-02-18 Whan-Hyuk Choi , Jon-Lark Kim