Barcode scans, clear phone calls, reliable data storage, satellite communication, and large-scale quantum computation are all made possible by error correction. We present a handbook version of The Error Correction Zoo, a curated reference of methods for protecting classical or quantum information from errors during storage and transmission. The handbook includes descriptions of these error-correcting codes and a classification according to the symbols they use. It also catalogues relations among codes and related objects such as sphere packings, lattices, designs, groups, and classical and quantum phases of matter. The collection is intended both as a rigorous reference and as a practical aid for tracing the web of code relationships and uncovering new connections.
翻译:条码扫描、清晰的电话通话、可靠的数据存储、卫星通信以及大规模量子计算,都得益于纠错技术。我们呈现《纠错码手册》版本,它是《纠错码动物园》的策展参考,收录了保护经典或量子信息在存储与传输过程中免受错误影响的方法。本手册包含这些纠错码的描述,并根据其使用的符号进行分类。同时,它还整理了码字之间的关系及其与球面堆积、格、设计、群、经典及量子物质相等相关对象之间的联系。本合集旨在作为严谨的参考工具,同时为追踪码字关系网络及发现新关联提供实用帮助。