This study addresses the use of Reed-Solomon error correction codes in QR codes to enhance resilience against failures. To fully grasp this approach, a basic cryptographic context is provided, necessary for understanding Reed-Solomon codes. The study begins by defining a code and explores key outcomes for codes with additional properties, such as linearity. The theoretical framework is further developed with specific definitions and examples of Reed-Solomon codes, presented as a particular variant of BCH codes. Additionally, the structure of QR codes is analyzed, encompassing different versions and how data is represented in the form of black and white pixels within an image. Finally, an inherent vulnerability of Reed-Solomon Codes, and particularly of QR codes, related to selective manipulation of modules is examined. This vulnerability leverages the error correction mechanisms present in Reed-Solomon codes.

翻译：本研究探讨了在QR码中运用里德-所罗门纠错码以提升抗故障能力的方法。为完整理解该技术路径，本文首先提供了理解里德-所罗门码所需的基础密码学背景。研究从编码的基本定义出发，探讨了具有线性等附加特性的编码体系的关键性质。通过将里德-所罗门码作为BCH码的特殊变体进行阐述，我们以具体定义和实例进一步构建了理论框架。此外，本文系统分析了QR码的结构体系，涵盖不同版本规格及其通过图像黑白像素实现数据编码的机制。最后，我们揭示了里德-所罗门码（特别是QR码）存在的固有安全漏洞——该漏洞源于对编码模块的选择性篡改，其攻击机理正是利用了里德-所罗门码内建的纠错机制。