Mathematics of QR Codes: History, Theory, and Implementation

Abstract

QR codes are a central part of the world today, bridging the physical and digital worlds through a simple, scannable pattern. Their uses are varied, ranging from displaying menus at a restaurant to product packaging. This essay explains the structure of QR codes, the error-correction mechanisms that ensure reliable decoding, and their variety of encoding modes and versions. It also discusses the concepts of Galois Fields and Reed-Solomon error correction underpinning the code. By exploring the design and inner workings of QR codes, it illustrates how structured patterns can efficiently store and transmit data. A link to sample code for generating QR codes is also provided.