Construction of multi-layered QR codes utilizing partitions of positive integers

Volume 18, Issue 3, pp 306--313 http://dx.doi.org/10.22436/jmcs.018.03.06 Publication Date: May 24, 2018       Article History

Authors

Passawan Noppakaew - Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand
Sukanya Khomkuth - Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand
Sureepat Sriwilas - Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand


Abstract

Multi-layered QR (MLQR) codes are created by superimposing many black and white QR codes, all of which are assigned their white areas with the colors in RGB color space. These colors must be different enough to enable distinguishing each layer of a MLQR code. This makes a MLQR code be able to hold more data than a common QR code. In this work, the procedures for generating and un-layering MLQR codes were proposed and the according graphical user interfaces (GUIs) were created with MATLAB. They use the property of a partition of the number 255, constructed by the geometric sequence \(\left\{2^{n-1}\right\}_{n\in\mathbb{N}}\), to compute the collection of suitable colors for assigning to black and white QR codes in the generating process. Our developed procedures can promote better intercommunication between human and computers, therefore ensure easier computer programming and being more flexible in the number of layers of created MLQR codes. We found that the developed GUIs could work accurately up to 15 layers because more QR code layers require the use of more colors, which diminish an ability to clearly distinguish the color of each QR code layer.


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