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This new handbook consolidates over 1,000 error-correcting codes into a rigorous reference linking classical and quantum information protection methods. By cataloging relationships between codes and underlying mathematical structures like lattices and groups, it serves as a practical resource for researchers tracing connections across storage, transmission, and computation domains. The open-source nature of the project invites community contributions to maintain accuracy and expand the taxonomy of these foundational technologies.
Handbook of Error-Correcting Codes
arXiv:2606.11484v1 Announce Type: new Abstract: 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.
Abstract: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.
440 classical codes, 619 quantum codes, 15 c-q codes. Online zoo at this https URL. Notify zookeeper of errors or issue a pull request at this https URL
Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)
arXiv:2606.11484 [quant-ph]
(or arXiv:2606.11484v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.11484 arXiv-issued DOI via DataCite (pending registration)
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