相关论文: Improved Methods For Generating Quasi-Gray Codes

In quasi-Monte Carlo methods, generating high-dimensional low discrepancy sequences by generator matrices is a popular and efficient approach. Historically, constructing or finding such generator matrices has been a hard problem. In…

In this note, I discuss results on integer compositions/partitions given in the paper "A Unified Approach to Algorithms Generating Unrestricted and Restricted Integer Compositions and Integer Partitions". I also experiment with four…

In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…

Quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set. It has been shown that this is possible for almost all choices of base sets and furthermore that…

A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, Graham, and Rhodes.…

The motivation of the current study was to design an algorithm that can speed up the processing of a query. The important feature is generating code dynamically for a specific query. We present the technique of code generation that is…

We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration…

Using an algebraic approach based on the theory of Coxeter groups, we design, and describe the performance of, a class of line codes for parallel transmission of $b$ bits over $b+1$ wires that admit especially simple encoding and decoding…

Being able to duplicate published research results is an important process of conducting research whether to build upon these findings or to compare with them. This process is called "replicability" when using the original authors'…

Graph Edit Distance (GED) is a widely used metric for measuring similarity between two graphs. Computing the optimal GED is NP-hard, leading to the development of various neural and non-neural heuristics. While neural methods have achieved…

Based on BRGC inspired order relations we give Gray codes and a generating algorithm for $q$-ary words avoiding a prescribed factor. These generalize an early 2001 result and a very recent one published by some of the present authors, and…

Code-switching is about dealing with alternative languages in speech or text. It is partially speaker-depend and domain-related, so completely explaining the phenomenon by linguistic rules is challenging. Compared to most monolingual tasks,…

Synthetic data used for scene text detection and recognition tasks have proven effective. However, there are still two problems: First, the color schemes used for text coloring in the existing methods are relatively fixed color key-value…

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit…

We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are…

A novel method guaranteeing nondecreasing girth is presented for constructing longer low-density parity-check (LDPC) codes from shorter ones. The parity-check matrix of a shorter base code is decomposed into N (N>=2) non-overlapping…

Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…

A combinatorial Gray code for a class of objects is a listing that contains each object from the class exactly once such that any two consecutive objects in the list differ only by a `small change'. Such listings are known for many…

Pseudo-random number generators (PRNG) are a fundamental element of many security algorithms. We introduce a novel approach to their implementation, by proposing the use of generative adversarial networks (GAN) to train a neural network to…

In this paper we show the usability of the Gray code with constant weight words for computing linear combinations of codewords. This can lead to a big improvement of the computation time for finding the minimum distance of a code. We have…