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  • https://doi.org/10.36676/irt.v11.i2.1630Copy DOI Icon

Math Behind QR Codes: Understanding Patterns and Data Storage

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Abstract

Quick Response codes, or QR codes, are already commonplace in our daily lives. We can use them to scan products in stores, visit websites, and pay using mobile apps. Although the majority of people often engage with QR codes, very few are fully aware of the underlying mathematics. The mathematical concepts underlying QR codes are examined in detail in this paper, along with the patterns, algorithms, and data storage systems that enable them. QR codes are two-dimensional barcodes that store information in a matrix format. It was intended to scan data quickly and reliably, making it ideal for mobile applications. QR codes, unlike standard one-dimensional barcodes, can hold data horizontally and vertically. This capability enables QR codes to store substantially more data than regular barcodes. A QR code stores data as a pattern of black and white squares, each encoding a binary value (1 or 0). These patterns are organized in a grid arrangement, with three huge squares at the corners to help the scanner establish the code's direction. The remaining grid holds the actual data, which is encoded as tiny squares. The mathematics underlying QR codes include the use of several techniques for error correction, encoding, and compression, ensuring that data is stored effectively and retrievable even if the code is broken or hidden.

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