相关论文: Decoding twisted permutation codes

We consider the problem of successive-refinement coding for lossy compression of individual sequences, namely, compression in two stages, where in the first stage, a coarse description at a relatively low rate is sent from the encoder to…

The Arithmetic is interpreted in all the groups of Richard Thompson and Graham Higman, as well as in other groups of piecewise affine permutations of an interval which generalize the groups of Thompson and Higman. In particular, the…

A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…

Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem…

In this paper, we introduce a class of twisted multiparameter singular integrals on $\mathbb{R}^{2m}$, motivated by the Cauchy--Szeg\H{o} projections and the solving operators for $\bar{\partial}_b$ on a broad family of quadratic surfaces…

Over the past years, Polar codes have arisen as a highly effective class of linear codes, equipped with a decoding algorithm of low computational complexity. This family of codes share a common algebraic formalism with the well-known…

Recently Liu, Long, Tong and Li [Phys. Rev. A 65, 022304 (2002)] have proposed a scheme for superdense coding between multiparties. This scheme seems to be highly asymmetric in the sense that only one sender effectively exploits…

Building upon the application of flags to network coding introduced by Liebhold, Nebe, and Vazquez-Castro, we develop a variant of this coding technique that uses degenerate flags. The information set is a metric affine space isometric to…

Artificial intelligence (AI) has revolutionized software engineering (SE) by enhancing software development efficiency. The advent of pre-trained models (PTMs) leveraging transfer learning has significantly advanced AI for SE. However,…

In this paper a wide family of identifying codes over regular Cayley graphs of degree four which are built over finite Abelian groups is presented. Some of the codes in this construction are also perfect. The graphs considered include some…

Following the approach by R. K\"otter and F. R. Kschischang, we study network codes as families of k-dimensional linear subspaces of a vector space F_q^n, q being a prime power and F_q the finite field with q elements. In particular,…

Dolfi, Guralnick, Praeger and Spiga asked if there exist infinitely many primitive groups of twisted wreath type with nontrivial coprime subdegrees. Here we settle this question in the affirmative. We construct infinite families of…

Computational predictions of mass spectra from molecules have enabled the discovery of clinically relevant metabolites. However, such predictive tools are still limited as they occupy one of two extremes, either operating (a) by fragmenting…

We introduce a block encoding method for mapping discrete subgroups to qubits on a quantum computer. This method is applicable to general discrete groups, including crystal-like subgroups such as $\mathbb{BI}$ of $SU(2)$ and $\mathbb{V}$ of…

An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear…

We introduce a new framework for solving an important class of computational problems involving finite permutation groups, which includes calculating set stabilisers, intersections of subgroups, and isomorphisms of combinatorial structures.…

The analysis of quantum algorithms which query random, invertible permutations has been a long-standing challenge in cryptography. Many techniques which apply to random oracles fail, or are not known to generalize to this setting. As a…

Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…

Arslan, Altoum, and Zaarour introduced an inversion statistic for generalized symmetric groups. In this work, we study the distribution of this statistic over colored permutations, including derangements and involutions. By establishing a…

We propose a quantitative notion of permutation stability for finitely generated groups. Our notion is related to, but distinct from, the ``stability rate'' introduced by Becker and Mosheiff (which is valid within the class of finitely…