scholarly journals On Pless symmetry codes, ternary QR codes, and related Hadamard matrices and designs

Author(s):  
Vladimir D. Tonchev
Keyword(s):  
2011 ◽  
Vol 10 (6) ◽  
pp. 2
Author(s):  
Sally Koch Kubetin
Keyword(s):  

Author(s):  
Gustavo Poot Tah ◽  
Erika Llanes Castro ◽  
José Luis López Martínez ◽  
Victor Chi Pech

This paper presents the design and development of a mobile application that uses QR codes for the inventory control of a computer center. This application was developed to support the administration of the computer center of the Multidisciplinary Unit Tizimin, with the aim to reduce costs and time of searching for articles when making an inventory, by leveraging the capabilities of smartphones and tablets. The implementation of the system was carried out using free software.


Author(s):  
N. A. Balonin ◽  
M. B. Sergeev ◽  
J. Seberry ◽  
O. I. Sinitsyna

Introduction: The Hadamard conjecture about the existence of Hadamard matrices in all orders multiple of 4, and the Gauss problem about the number of points in a circle are among the most important turning points in the development of mathematics. They both stimulated the development of scientific schools around the world with an immense amount of works. There are substantiations that these scientific problems are deeply connected. The number of Gaussian points (Z3 lattice points) on a spheroid, cone, paraboloid or parabola, along with their location, determines the number and types of Hadamard matrices.Purpose: Specification of the upper and lower bounds for the number of Gaussian points (with odd coordinates) on a spheroid depending on the problem size, in order to specify the Gauss theorem (about the solvability of quadratic problems in triangular numbers by projections onto the Liouville plane) with estimates for the case of Hadamard matrices. Methods: The authors, in addition to their previous ideas about proving the Hadamard conjecture on the base of a one-to-one correspondence between orthogonal matrices and Gaussian points, propose one more way, using the properties of generalized circles on Z3 .Results: It is proved that for a spheroid, the lower bound of all Gaussian points with odd coordinates is equal to the equator radius R, the upper limit of the points located above the equator is equal to the length of this equator L=2πR, and the total number of points is limited to 2L. Due to the spheroid symmetry in the sector with positive coordinates (octant), this gives the values of R/8 and L/4. Thus, the number of Gaussian points with odd coordinates does not exceed the border perimeter and is no less than the relative share of the sector in the total volume of the figure.Practical significance: Hadamard matrices associated with lattice points have a direct practical significance for noise-resistant coding, compression and masking of video information.


Author(s):  
Widyasari Widyasari ◽  
Hadi Sutopo ◽  
Murniati Agustian

Mathematics in elementary school is difficult to understand, boring, formal, theoretical, and book-based learning, which makes students tired of listening and paying attention. The purpose of this study is to create a learning prototype based on QR codes, especially mathematics learning in elementary schools. Using the QR code, students can access math games related to the course. This learning model could encourage students to learn mathematics. The research included seven steps in research and development named after Borg & Gall, such as need assessment, plan, early product development, first test, revise early product, field test and revise product. The object of the research is QR code-based learning, and the respondents are elementary school students and teachers. After analyzing data in the first and field test, researchers found the result. QR code-based learning could support children for learning mathematics.


Author(s):  
Mingliang Xu ◽  
Qingfeng Li ◽  
Jianwei Niu ◽  
Hao Su ◽  
Xiting Liu ◽  
...  

Quick response (QR) codes are usually scanned in different environments, so they must be robust to variations in illumination, scale, coverage, and camera angles. Aesthetic QR codes improve the visual quality, but subtle changes in their appearance may cause scanning failure. In this article, a new method to generate scanning-robust aesthetic QR codes is proposed, which is based on a module-based scanning probability estimation model that can effectively balance the tradeoff between visual quality and scanning robustness. Our method locally adjusts the luminance of each module by estimating the probability of successful sampling. The approach adopts the hierarchical, coarse-to-fine strategy to enhance the visual quality of aesthetic QR codes, which sequentially generate the following three codes: a binary aesthetic QR code, a grayscale aesthetic QR code, and the final color aesthetic QR code. Our approach also can be used to create QR codes with different visual styles by adjusting some initialization parameters. User surveys and decoding experiments were adopted for evaluating our method compared with state-of-the-art algorithms, which indicates that the proposed approach has excellent performance in terms of both visual quality and scanning robustness.


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