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We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a…

Symbolic Computation · Computer Science 2010-09-09 Jean-Guillaume Dumas , Thierry Gautier , Jean-Louis Roch

We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a…

Symbolic Computation · Computer Science 2010-01-26 Jean-Guillaume Dumas , Thierry Gautier , Jean-Louis Roch

This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…

Number Theory · Mathematics 2013-09-03 W. H. Ko

Ananda Mohan suggested that the first New Chinese Remainder Theorem introduced by Wang can be derived from the constructive proof of the well-known Chinese Remainder Theorem (CRT) and claimed that Wang's approach is the same as the one…

Other Computer Science · Computer Science 2009-03-23 Jean-Luc Beuchat

Interactive image restoration aims to generate restored images by adjusting a controlling coefficient which determines the restoration level. Previous works are restricted in modulating image with a single coefficient. However, real images…

Image and Video Processing · Electrical Eng. & Systems 2020-09-23 Jingwen He , Chao Dong , Yu Qiao

In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduce redundancy to ensure recoverability from failure. To get the most out of every byte, practitioners and theorists have…

Information Theory · Computer Science 2026-02-26 Joshua Brakensiek , Venkatesan Guruswami

In this paper, new results on convolution of spectral components in binary fields have been presented for combiatorial sequences. A novel method of convolution of DFT points through Chinese Remainder Theorem (CRT) is presented which has…

Information Theory · Computer Science 2019-11-27 Muhammad Asad Khan , Sajid Saleem , Amir A Khan

In this paper, we derive new computational techniques for residue number systems (RNS) based Barrett algorithm (BA). The focus of the work is an algorithm that carries out the entire computation using only modular arithmetic without…

Number Theory · Mathematics 2016-02-05 Hari K. Garg , Hanshen Xiao

High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using…

Hardware Architecture · Computer Science 2024-03-21 Weihang Tan , Sin-Wei Chiu , Antian Wang , Yingjie Lao , Keshab K. Parhi

Using an adaptation of Qin Jiushao's method from the 13th century, it is possible to prove that a system of linear modular equations a(i,1) x(i) + ... + a(i,n) x(n) = b(i) mod m(i), i=1, ..., n has integer solutions if m(i)>1 are pairwise…

History and Overview · Mathematics 2012-06-25 Oliver Knill

The Minimum Covariance Determinant (MCD) approach robustly estimates the location and scatter matrix using the subset of given size with lowest sample covariance determinant. Its main drawback is that it cannot be applied when the dimension…

Methodology · Statistics 2021-01-13 Kris Boudt , Peter J. Rousseeuw , Steven Vanduffel , Tim Verdonck

In this paper we present two efficient methods for reconstructing a rational number from several residue-modulus pairs, some of which may be incorrect. One method is a natural generalization of that presented by Wang, Guy and Davenport in…

Number Theory · Mathematics 2015-07-22 John Abbott

An MV-algebra (equivalently, a lattice-ordered Abelian group with a distinguished order unit) is strongly semisimple if all of its quotients modulo finitely generated congruences are semisimple. All MV-algebras satisfy a Chinese Reminder…

Logic · Mathematics 2013-06-19 Vincenzo Marra

Compared with co-prime integers, co-prime integer matrices are more challenging due to the non-commutativity. In this paper, we present a new family of pairwise co-prime integer matrices of any dimension and large size. These matrices are…

Signal Processing · Electrical Eng. & Systems 2025-04-14 Guangpu Guo , Xiang-Gen Xia

Augmenting the balanced residue number system moduli-set $\{m_1=2^n,m_2=2^n-1,m_3=2^n+1\}$, with the co-prime modulo $m_4=2^{2n}+1$, increases the dynamic range (DR) by around 70%. The Mersenne form of product $m_2 m_3 m_4=2^{4n}-1$, in the…

Hardware Architecture · Computer Science 2024-12-12 Ghassem Jaberipur , Bardia Nadimi , Jeong-A Lee

Recently, experiments have been reported where researchers were able to perform high dynamic range (HDR) tomography in a heuristic fashion, by fusing multiple tomographic projections. This approach to HDR tomography has been inspired by HDR…

Information Theory · Computer Science 2021-05-11 Matthias Beckmann , Ayush Bhandari , Felix Krahmer

Data replication is used in distributed systems to maintain up-to-date copies of shared data across multiple computers in a network. However, despite decades of research, algorithms for achieving consistency in replicated systems are still…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-08-30 Victor B. F. Gomes , Martin Kleppmann , Dominic P. Mulligan , Alastair R. Beresford

The critical point for the successes of spectral-type subspace clustering algorithms is to seek reconstruction coefficient matrices which can faithfully reveal the subspace structures of data sets. An ideal reconstruction coefficient matrix…

Machine Learning · Computer Science 2022-08-01 Lai Wei , Shiteng Liu , Rigui Zhou , Changming Zhu

The matrix completion problem provides a unifying lens through which many fundamental problems in coding theory can be viewed. In this paper, we investigate Locally Recoverable Codes (LRCs) with Maximal Recoverability (MR) and Maximum…

Information Theory · Computer Science 2026-04-24 Sakshi Dang , Julia Lieb , Pedro Soto , Alex Sprintson

In this work, our main objective is to construct quantum codes from quasi-twisted (QT) codes. At first, a necessary and sufficient condition for Hermitian self-orthogonality of QT codes is introduced by virtue of the Chinese Remainder…

Information Theory · Computer Science 2020-01-07 Jingjie Lv , Ruihu Li , Junli Wang