Handbook of Error-Correcting Codes
For researchers and practitioners in coding theory, quantum computing, and related fields, this handbook provides a comprehensive, organized reference to navigate the landscape of error-correcting codes and their interrelations.
This paper presents a handbook version of The Error Correction Zoo, a curated reference cataloging classical and quantum error-correcting codes, their classifications, and relationships to other mathematical objects. The collection serves as both a rigorous reference and a practical tool for exploring code connections.
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.