Quantum Codes from Generalized Reed-Solomon Codes and Matrix-Product Codes

One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized Reed-Solomon codes. We also present some classes of quantum codes from matrix-product codes. It turns out that many of our quantum codes are new in the sense that the parameters of quantum codes cannot be obtained from all previous constructions

Private Information Retrieval from MDS Coded Databases with Colluding Servers under Several Variant Models

Private information retrieval (PIR) gets renewed attentions due to its information-theoretic reformulation and its application in distributed storage system (DSS). The general PIR model considers a coded database containing $N$ servers storing $M$ files. Each file is stored independently via the same arbitrary $(N,K)$-MDS code. A user wants to retrieve a specific file from the database privately against an arbitrary set of $T$ colluding servers. A key problem is to analyze the PIR capacity, defined as the maximal number of bits privately retrieved per one downloaded bit. Several extensions for the general model appear by bringing in various additional constraints. In this paper, we propose a general PIR scheme for several variant PIR models including: PIR with robust servers, PIR with Byzantine servers, the multi-file PIR model and PIR with arbitrary collusion patterns.Comment: The current draft is extended by considering several PIR models. The original version named "Multi-file Private Information Retrieval from MDS Coded Databases with Colluding Servers" is abridged into a section within the current draft. arXiv admin note: text overlap with arXiv:1704.0678

Snake-in-the-Box Codes for Rank Modulation under Kendall's τ\tau-Metric

For a Gray code in the scheme of rank modulation for flash memories, the codewords are permutations and two consecutive codewords are obtained using a push-to-the-top operation. We consider snake-in-the-box codes under Kendall's $\tau$-metric, which is a Gray code capable of detecting one Kendall's $\tau$-error. We answer two open problems posed by Horovitz and Etzion. Firstly, we prove the validity of a construction given by them, resulting in a snake of size $M_{2n+1}=\frac{(2n+1)!}{2}-2n+1$. Secondly, we come up with a different construction aiming at a longer snake of size $M_{2n+1}=\frac{(2n+1)!}{2}-2n+3$. The construction is applied successfully to $S_7$.Comment: arXiv admin note: text overlap with arXiv:1311.4703 by other author

Quantum Block and Synchronizable Codes Derived from Certain Classes of Polynomials

One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical codes, we are able to obtain some new quantum codes. It turns out that some of quantum codes exhibited here have better parameters than the ones available in the literature. Meanwhile, we give a new class of quantum synchronizable codes with highest possible tolerance against misalignment from duadic codes.Comment: 9 pages. arXiv admin note: text overlap with arXiv:1403.6192, arXiv:1311.3416 by other author

A general private information retrieval scheme for MDS coded databases with colluding servers

The problem of private information retrieval gets renewed attentions in recent years due to its information-theoretic reformulation and applications in distributed storage systems. PIR capacity is the maximal number of bits privately retrieved per one bit of downloaded bit. The capacity has been fully solved for some degenerating cases. For a general case where the database is both coded and colluded, the exact capacity remains unknown. We build a general private information retrieval scheme for MDS coded databases with colluding servers. Our scheme achieves the rate $(1+R+R^2+\cdots+R^{M-1})$, where $R=1-\frac{{{N-T}\choose K}}{{N\choose K}}$. Compared to existing PIR schemes, our scheme performs better for a certain range of parameters and is suitable for any underlying MDS code used in the distributed storage system.Comment: Submitted to IEEE Transactions on Information Theor

GHZ States, Almost-Complex Structure and Yang--Baxter Equation (I)

Recent study suggests that there are natural connections between quantum information theory and the Yang--Baxter equation. In this paper, in terms of the generalized almost-complex structure and with the help of its algebra, we define the generalized Bell matrix to yield all the GHZ states from the product base, prove it to form a unitary braid representation and present a new type of solution of the quantum Yang--Baxter equation. We also study Yang-Baxterization, Hamiltonian, projectors, diagonalization, noncommutative geometry, quantum algebra and FRT dual algebra associated with this generalized Bell matrix.Comment: 17 pages, late

Design of the Helium Purifier for IHEP-ADS Helium Purification System

Helium Purification System is an important sub-system in the Accelerator Driven Subcritical System of the Institute of High Energy Physics(IHEP ADS). The purifier is designed to work at the temperature of 77K. The purifier will work in a flow rate of 5g/s at 20MPa in continuous operation of 12 hours. The oil and moisture are removed by coalescing filters and a dryer, while nitrogen and oxygen are condensed by a phase separator and then adsorbed in several activated carbon adsorption cylinders. After purification, the purified helium has an impurity content of less than 5ppm

Invertible binary matrix with maximum number of 22-by-22 invertible submatrices

The problem is related to all-or-nothing transforms (AONT) suggested by Rivest as a preprocessing for encrypting data with a block cipher. Since then there have been various applications of AONTs in cryptography and security. D'Arco, Esfahani and Stinson posed the problem on the constructions of binary matrices for which the desired properties of an AONT hold with the maximum probability. That is, for given integers $t\le s$, what is the maximum number of $t$-by-$t$ invertible submatrices in a binary matrix of order $s$? For the case $t=2$, let $R_2(s)$ denote the maximal proportion of 2-by-2 invertible submatrices. D'Arco, Esfahani and Stinson conjectured that the limit is between 0.492 and 0.625. We completely solve the case $t=2$ by showing that $\lim_{s\rightarrow\infty}R_2(s)=0.5$

Automated Spectral Classification of Galaxies using Machine Learning Approach on Alibaba Cloud AI platform (PAI)

Automated spectral classification is an active research area in astronomy at the age of data explosion. While new generation of sky survey telescopes (e.g. LAMOST and SDSS) produce huge amount of spectra, automated spectral classification is highly required to replace the current model fitting approach with human intervention. Galaxies, and especially active galactic nucleus (AGNs), are important targets of sky survey programs. Efficient and automated methods for galaxy spectra classification is the basis of systematic study on physical properties and evolution of galaxies. To address the problem, in this paper we carry out an experiment on Alibaba Cloud AI plaform (PAI) to explore automated galaxy spectral classification using machine learning approach. Supervised machine learning algorithms (Logistic Regression, Random Forest and Linear SVM) were performed on a dataset consist of ~ 10000 galaxy spectra of SDSS DR14, and the classification results of which are compared and discussed. These galaxy spectra each has a subclass tag (i.e. AGNs, Starburst, Starforming, and etc.) that we use as training labels.Comment: 4 pages, presented at the Astronomical Data Analysis Software and Systems (ADASS) XXVII conference, Santiago, Chile, October 201

A Fast and Practical Method to Estimate Volumes of Convex Polytopes

The volume is an important attribute of a convex body. In general, it is quite difficult to calculate the exact volume. But in many cases, it suffices to have an approximate value. Volume estimation methods for convex bodies have been extensively studied in theory, however, there is still a lack of practical implementations of such methods. In this paper, we present an efficient method which is based on the Multiphase Monte-Carlo algorithm to estimate volumes of convex polytopes. It uses the coordinate directions hit-and-run method, and employs a technique of reutilizing sample points. The experiments show that our method can efficiently handle instances with dozens of dimensions with high accuracy